I think that you would benefit from a basic physical mechanics course, but I think I get what you are trying to say. I hope all of this isnt too arcane for you.
First, I think you are talking about turning heat into electricity. Remember that energy is a very loose term. So, could we turn this heat into electricity, yes, of course we can. There are in fact semiconductor devices that do just that. If you apply a current to them they heat up, and if you draw current out of them they cool down. You see these used in medical devices and lab environments where there is a requirement to maintain a constant temperature in a system.
The big problem with how you are viewing this is the principle of conservation of energy. Heat is just a measure of energy in a given system. If you were to remove this heat to make electricity, you would reduce the amount of energy in the system and the object would get colder. You would need an outside source to replenish this heat, or you would rapidly run out of energy in the system.
Take the example of the turbine I mentioned earlier. A turbine does not generate electricity from the difference in heat, as you said. Rather, a turbine is simply converting potential energy, in the form of heat, into mechanical force used to turn a generator. Turbines need not be diriven directly by heat either. Hydro-electric plants use turbines, as do some wind farms.
However, lets stay with a heat driven turbine. A nuclear reaction is a great source of heat energy. If this reaction occurs in a tank of water, the water will become super-heated and turn to steam. This steam, which has now expanded in size and therefore pressure, can be used to do the mechanical work of turning the turbine. It looses some of its heat in the process, and is eventually condensed and returned to the tank where it is re-heated by the nuclear reaction. Conservation of energy has not been violated because the total energy of the system, including the electricity generated is still the same.
Doing something similar to power generation at this scale in the nano world becomes tricky. First of all, you cant use magnets and coils for motors or power generation (which is just a motor in reverse), because transient inductance in the wire tend to eliminate any electro-motive force you hope to generate. As if that werent bad enough, even the small resistances of wires start to play a huge part, and we have yet to find any viable super-conducting material that operates at anything approaching room temperature.
Also, if you wanted to rectify the source voltage you would have a problem with the diodes. The best diodes available have a voltage drop of .3V and an internal resistance of about 10k Ohms. Any AC that you dumped into them would be dissipated as heat, provided you could even overcome the voltage drop.
Its a great idea you have there, but I dont think investors will be lining up any time soon. But if you figure it out I will certainly be on board.