Would it be possible to reenter the atmosphere without a heat shield using a glider design? Say my vehicle currently in orbit had large wings that would provide the necessary lift, would it be possible to bleed off the energy so slowly and gradually lose altitude that no heat shield would be required? I was thinking that even at the low pressure at high altitude, the wings along with the high velocity would prevent the craft from falling rapidly. And thus keep the drag(thinner atmosphere at higher altitude) minimal and so the experienced heating would be manageable.
 A: I hope I didn't make a mistake in this quick back-of-the-envelope calculation, but:
A vehicle mass of $7.8*10^4 kg$ and an orbital velocity of $2.8*10^4 km/h (\stackrel{\wedge}{=} 7,78*10^3 m/s)$ result in a kinetic energy of $2.35*10^{12} J$, i.e. more than two terajoule. That's quite a bit of energy if you consider that a nuclear power plant's output is measured in gigawatt and hence would need to run for many minutes to produce this energy (and, incidentally, corroborates the anecdote that the first stage of a Saturn V burned more fuel than all of Great Britain).
The potential energy of a 500 km orbit should be around $3.8*10^{11}J,$ that is about 1/8 or so of the kinetic energy. The combined energy that must be shed is $2.74*10^{12}J.$
The average heat dispersal rate during a 30 minute (= 1800s) descent then is $1.52*10^9W$, which is the output of your standard average nuclear power plant block. The air cooling during re-entry works really well (the word "air cooling" never before entered my mind when I imagined re-entry).
If you want to bring the power down to an order of magnitude which can be handled without a heat shield, say, 1 MW = $1*10^6W$ (but doesn't that still sound hot?), you need to stretch the descent by a factor of 1,000.
The descent would no longer take 30 minutes but 30,000 minutes, or about 20 days.
It's not surprising that landing the second stage proved harder than envisioned.
Perhaps the 1 MW assumption is too pessimistic though: After all, Falcon 9's first stage descends without a real heat shield and only some half-arsed entry burn. Differences:

*

*The initial velocity is only around 6000 - 8,000km/h, that is, less than 1/3 of an orbiting vehicle; the kinetic energy, which grows quadratic, is therefore less than 1/10 for the same mass, which makes it less than 1/20, assuming a weight of $3*10^4kg$ for an almost-empty first stage.

*The entry burn reduces the velocity to about 600 m/s. Together with the lower mass of perhaps 30,000 kg (including landing-burn fuel) this results in a  kinetic energy of $5.4*10^9J$, and with 80 seconds to go after that we arrive at a heat dispersal rate of $6.75*10^7W$, or 67 MW. Still, good air-cooling.

If we take that as an indication for what a largely unshielded vehicle can sustain we may de-orbit not in 20 days but instead within 1/60 of that, i.e. 8 hours or so. But it may well be that a vehicle that can take a certain degree of heat on its outer shell for a minute would overheat when exposed to it for many hours. On the other hand,  large wings or canopies — constructive and mass issues aside — would distribute the heat load more. The truth may be in the middle.
From pureley energetic considerations, a de-orbiting time of many hours is a likely scenario.
A: Accepting for the sake of argument that it's possible to build a glider that can generate meaningful lift in a near-vacuum, a slow gliding reentry is actually worse for heat buildup than a fast ballistic reentry.
One of the key discoveries of the early 1950s was that a blunt reentry vehicle is superior to a streamlined one.  During a blunt-body reentry, most of the vehicle's orbital energy is shed as adiabatic compression of the air in a shock wave slightly ahead of the vehicle; very little goes into friction heating of the vehicle.  The main source of heating is radiative heating from the shock wave, and the main purpose of the heat shield is to protect the vehicle from this heat for a few minutes.
Since the vehicle's orbital energy is mostly going in to the air around it, this means that the faster you can stop, the less heat you need to deal with.  The Mercury capsules with their crushing 12 g reentry profiles needed far less heat shielding than the Apollo capsules, which entered with a more comfortable 4 g peak acceleration.
A slow, gliding reentry goes to the other extreme: the hypersonic shock wave is formed on the surface of the vehicle, maximizing heat transfer.  You need to make your reentry really gradual to keep the heat load reasonable; Peter's answer suggests that you're looking at multi-day reentry periods.
A: Being in orbit isn't about going very high, it's about going sideways very fast. In order to get to orbit, about 80% of the energy is used in achieving orbital speed, which only 20% is used in getting to orbital altitude. A re-entering craft needs to rid itself of its kinetic energy, but you can see that most of that energy actually doesn't come from its descent through the atmosphere - it already has most of that kinetic energy even before it starts to descend. Once you're in orbit at an altitude of 100km, your kinetic energy is 30x greater than your potential energy - the kinetic energy gained by falling to the ground is a mere few percent of the kinetic energy you already have.
A re-entering glider could have a slower vertical descent, but that won't really matter. It will still have a massive amount of kinetic energy due to its high horizontal orbital speed. Having a more controlled vertical descent won't really change much about re-entry, as the real issue is eliminating the horizontal velocity, which a glider won't help with at all.
You could potentially spend time in the upper atmosphere to bleed off speed before entering the thicker atmosphere which causes significant heating, but
this question over at Space Exploration suggests that a wing that could provide sufficient lift in such low pressure would be impossibly large. Getting sufficient lift to remain airborne is going to be extremely difficult at high altitudes.
A: You have to bear some fundamental physical principles in mind here:
An orbiting satellite that is only experiencing atmospheric drag (like a spherical or irregularly shaped object) will gradually lose height but increase its speed in the process (closer orbits have higher speeds). This is of course the last thing you want in this case. In order to reduce the speed you have to prevent the spacecraft from losing much height by also having an aerodynamic lift. For this you need a suitably shaped object or wing orientated such that the lift force is comparable to the drag force. For a plane surface the two forces are equal for an angle of 45 deg relative to the direction of motion. The space shuttle for instance used to enter the atmosphere with the nose pitched up by 40 deg, so almost equal lift and drag forces. This resulted then only in a rather slow height decrease (the space shuttle took about 8000 km horizontal distance to drop just 130 km).
So basically, what you want here is a speed reduction whilst more or less staying at the same height. In principle, you could reduce the horizontal speed to zero this way. With an airplane this would be called stalling (a situation you usually want to avoid), but in this case it would be the solution of your problem, provided you do this at a height where the drag (and lift) is not so strong that you need a heat shield. You would then of course fall right down, but the speed you achieve falling from 200 km or so would be quite moderate and hardly require any heat shield either. And when you have picked up some speed, you could re-orientate the spacecraft and land it like an airplane (like the space shuttle did).
Having said this, your suggested glider re-entry without heat shield has actually already been done almost 20 years ago with the SpaceShipOne using a shape-changing airfoil design, but this was a suborbital (ballistic) trajectory, reaching about 100 km height but only a speed of about Mach 3.
A: The key insight here is that you have a lot of energy, and all that energy has to be turned into heat. There's no other way to lose it. Your goal is 0 m/s at 0 km height. It doesn't really matter what the original proportion of kinetic versus potential energy is, both need to be turned into heat, and that heat needs to be shed.
Heat shields are very effective ways of getting rid of the heat. Ablative heat shields do so by burning up, other heat shields take advantage of the fact that radiative cooling increases with the fourth power of the temperature.
The idea of a glider is that you'd shed the heat slowly, by taking more time for the descent. You still need to shed the same amount of heat energy, but the power is inversely proportional to the available time. That's only a first power, though.
The engineering problem with the idea is that you need to generate lift at hypersonic speeds, without generating too much drag. That drag generates friction and thus heat, which was exactly what we're trying to reduce. But without lift, you'd fall too fast.
That lift needs to be fairly constant (slightly smaller than your weight), despite the deceleration. Else, you'd accelerate further or bounce back into space. And the Centre of Lift also needs to remain fairly stable despite the deceleration, or you'd tip over. You can't pump fuel around like Concorde did to shift the Centre of Gravity to match the CoL.
A: Nope, can't be done. The problem being there are two things you have to come to terms with, earths gravitational field and its atmosphere. The first forces you to obtain an orbit. From there, every way down is in an angle. The usable angle of reentry is relatively small. Dig in too deep and you'll burn up. Come in too shallow and you'll just bounce off, back into space.
An orbiting shuttle slows down its orbiting speed to start a fall in that angle. That fall continues until its airspeed is slow enough to allow it to fly, gliding down to the surface. The choice of the direction of that angle aims to minimize the friction during the fall. Going from burning up on reentry to 'just' needing a heat shield is already quite an achievement. The idea that it would be possible to enter earths gravitational field and then just gently glide all the way down to the surface without ever getting hot is not realistic.
