Ionization by heating I would like to ask what happens if an atom exposed to a very high temperature - say millions of degrees (Kelvin). Can we use heating to separate electrons from their nucleus? And what happens to the nucleus if its electrons are stripped off?
Thank you,
 A: By a high temperature we just mean that the particles in our gas are moving rapidly. The velocity of the particles is related to the temperature by the Maxwell-Boltzmann distribution (though note this only applies to temperatures where the velocities are non-relativistic).
Anyhow, once the velocities of the atoms are high enough that the collision energy is greater than the ionisation energy the collisions will start ionising the atoms, and we'll end up with a plasma. Get the temperature high enough and, in principle at least, you could completely ionise the atoms.
As for what happens to the nuclei with the electrons gone, well, not much. We routinely generate beams of fully ionised atoms in particle accelerators, though not by heating them. Typically atoms are partially ionised, accelerated then passed through a carbon film. The collision with the carbon scatters the electrons, but because the nuclei are heavier they go straight through and we get a beam of nuclei out the other side.
Anyhow, the nuclei just behave like large positively charged particles. We can even collide them, which is done in the RHIC and the LHC.
A: To produce electrons one simply heats up a piece of metal, and they come
boiling off. If you want a beam of electrons, you just set up a positively charged plate
nearby, to attract them over, and poke a small hole in it; the electrons that make it
through the hole constitute the beam. Such an electron gun is the starting element
in a television tube or an oscilloscope or an electron accelerator.$_1$  
So, we can strip off, some of the electrons from the atom. It is difficult to say whether we can really make the atom completely nude, as I am not good at QM.

Credits: $_1$Introduction to Elementary Particles-David Griffiths-Pg.No.4-2nd Edition.
A: 
Can we use heating to separate electrons from their nucleus?

With the following 'conversion factor' between temperature and energy:
$$
{1 \over k_{\text{B}}} \approx 11600 \, \text{K/eV}
$$
you'll see that 1'000'000 Kelvin corresponds an average energy of about 86 eV, much more than enough to fully ionize (separate the electron from the nucleus) e.g. Hydrogen atoms (whose ionization energy is 13.6 eV).

And what happens to the nucleus if its electrons are stripped off?

For example the binding energy of a Helium nucleus ($^4$He) is about 28'300'000 eV, much larger than the 86 eV, so when the Helium nuclei collide, the collision energy is not enough to break the nucleus apart in most cases. 

By the way, a cathode ray tube TV uses a heated filament (similar to an incandescent light bulb whose filament has a typical temperature of 2500 deg Celsius) to 'lift' (some) of the electrons from a bound state to the free (unbound) state and then accelerates them with a voltage of about 10-20 kVolts. This is much more effective than to create a temperature of millions of degrees. 
It's true that with an ionization energy of Tungsten of 7.9 eV with the above conversion factor one would calculate a temperature of almost 100'000 Kelvin for ionization. However, keep in mind that this is the average temperature, the variation in energy of the atoms is quite large, so some electrons are already stripped of their nucleus at lower temperature and the high voltage between the filament and the screen then quickly moves them away from the filament.
