Since it is burning fuel that makes heat, the chemical reaction that needs to be reversed is to "unburn" stuff. This is rather difficult to do, as the only practical ways to unburn things are to use intense heat or to use electricity. Electricity is the most efficient and controllable way of doing it, for example by splitting water by electrolysis into hydrogen and oxygen. Once you have hydrogen you can burn it to get the energy back, or you can feed it into a fuel cell to make electricity directly.
Overall, electrolysis and fuel cells is the direction most people are looking at.
There are possibilities using heat instead of electricity, but they have more technical challenges, especially because of the high temperatures required.