Will the earth never cool, but only get hotter? Since the earth is in a vacuum and therefore there is no thermal transfer of heat to anything else, how can it even cool down?  It seems like its average temperature would always be constant, ignoring outside sources of heat.
However, if you then consider that there is constant radiant heat transfer from the sun to the earth, now you have a net gain in energy/heat.
I also read somewhere that the solar wind actually blows a bit of our atmosphere into space, but that seems like a miniscule amount of heat loss compared to how much heat is gained from the sun.
Will the earth ever cool at all?
 A: All matter radiates electromagnetic radiation according to its temperature. It is called black body radiation.
The power emitted goes  as T^4 , where T is the temperature in degrees Kelvin. 
If there is no replenishment of the energy lost the body in vacuum will approach absolute zero after a calculable time. 
The earth gets replenished mainly  by the sun, a bit from internal fission too.

Absolute zero cannot be reached in finite steps as this formulation of the third law of thermodynamics states:

It is impossible for any process, no matter how idealized, to reduce the entropy of a system to its zero point value in a finite number of operations.

A: You've pointed out that the sun carries out radiant heat transfer to the Earth, but you've forgotten that the earth also radiates heat into space. This is how the Earth cools down.
A: 
"Since the earth is in a vacuum and therefore there is no thermal
  transfer of heat"
"there is constant radiant heat transfer from the sun to the earth"

You might like to think about those two statements !
Since the rate of heat flow from the earth into space increase as the temperature increases then you have a stable equilibrium. If the earth got hotter, more energy would be radiated into space cooling it. If the earth got cooler,less energy is radiated - heating it.
A: As Martin above suggested, the Earth actually loses as much heat through thermal radiation as it gains through radiation from the Sun each day. The assumption that leads us to that conclusion is basically that the Earth is in thermal equilibrium with its surroundings. If the Sun suddenly started pumping out more heat, the Earth would eventually adjust until equilibrium is reattained, at a higher temperature. How could humans affect that temperature? The easiest way to understand how the global temperature could change is to consider clouds. With more clouds, a chunk of the Earths radiation is reflected back, meaning less is radiated outward. The temperature adjusts up until we radiate out as much as the Sun radiates in again. Of course also the Sun's energy radiating in is less (some gets reflected) but the net effect is temperature rise -if clouds both cut the Sun's radiation in and our radiation out by 10%, we are still in equilibrium but we are still stuck with our 10% of heat reflected back at us.-
The energy coming in from the Sun is low entropy, which means it is useful to do work (such as power a plants chemical reactions). The energy that leaves is high entropy (read random, disordered like the motion of hot gas particles) that is no longer very useful to do work. So it is sometimes said that the Sun doesn't really provide us with energy (we end up with no more energy than we started) but with low entropy. This is described in more details in the answers of this question: The Sun is giving us a low entropy, not energy
