how does heat energy start to speed up a gas molecule? If it was possible to place a single gas molecule in a cell and freeze it to near absolute zero.
  What would the molecule do as it thawed out?
Would it translate the heat energy into it's electrons and nucleus into vibrations and remain where it was? Would these vibrations cause it to start bouncing off the floor until it gets enough speed to convert the heat into kinetic energy?
Do gas molecules need convection to start speeding them up ( like the atmosphere), or do they translate heat into kinetic energy straight away all by themselves?
 A: The question of molecular motion in response to "heat" is answered by statistical mechanics. If you have a single molecule at a temperature T, all that means is that the probability of any state of the molecule with energy E is as likely as $e^{-E\over T}$.
For the nucleus to move, it must change it's energy state by a discrete amount, and the gap between the lowest energy state and any of the excited states is thousands of eV's. In temperature units, this is millions of degrees. So the nucleus will have negligible probability to get excited at normal temperatures.
The electrons are excited in the energy range of .1-1eV, which is about 300-30000 degrees. So again, you won't get significant electronic excitations.
The rotational or bending energies of the molecule can start to get excited at relatively small temperatures, if the molecule is large, so easy to bend and rotate slowly. But the significant thing is center of mass motion. The energy levels of moving around depend on the size of the box, and if the box is arbitrarily big, these levels have energies that are arbitrarily small. So the molecule will, at low temperatures, start to move around first, before it rotates or deforms, or does anything electronic or nuclear.
The notion of a thermal ensemble for a single molecule is well defined statistically, so long as you ask about average properties over many trials, rather than single trials.
A: I don't think the definition of heat can be used down to the molecular level, as it is a macroscopic measure for the average vibrational energy of the different molecules. In the  same way, you cannot define freezing for a single molecule as it describes a phase change, which you can only describe using a bunch of molecules.
Suppose you have a set-up that is capable of extracting all energy to "freeze" it, then there is also no vibration. Putting "heat" into the system is the same thing as adding vibrations to the molecule. So this comes from outside the molecule, not from the inside.
Convection is caused by the net displacement (flow) of molecules from one location to the other. Suppose you have a bunch of molecules, which are not of the same temperature, than diffusion will be the mechanism of heat transfer to surrounding molecules.
So it all comes down to: what is heat precisely, and that is a difficult to relate from macroscopic to molecular scales.
