I had an idea for a new type of battery which recharges off of heat. I was wondering if it was possible. I haven't worked out any specifics yet, though.
A mixture of two chemicals has an endothermic reaction. The reaction produces two ionized chemicals (say salts) which are less stable than the first two chemicals. Metal plates can be used to draw electricity from the salts (actually drawing electrons from the plates, but whatever), causing the salts to recombine into the original two chemicals.
I had the idea while trying to figure out how to turn heat into electricity more efficiently. I realized that endothermic reactions are good at absorbing heat, though they don't release it as electricity.