Recharge battery using heat A galvanic cell works by having two electrochemical equilibriums which have a different potential. 

If you (theoretically) had a galvanic cell with two electrodes which have almost identical potentials and are sensitive to heat (at the anode the oxidation is exothermic and at the cathode the reduction is), connected the two half cells with a diode contrary to the normal current and heated the whole thing up, shouldn't it be possible to reverse the current and recharge the cell?

Please excuse language mistakes I might have made; I am not a native English speaker and therefore don't know all technical terms in English.
An electrochemical cell works on the principle that the Gibbs free energy gets converted into electrical energy by making the electron transfer indirect. This is done by itself to make the 'heat energy' that would normally be released in a redox reaction into 'electrical energy' so ideally heat shouldn't be lost. 

Also you say you want to charge the cell by heating it so as to make the reaction go in the opposite direction. But for a spontaneous cell reaction, increasing the temperature makes the Gibbs free energy more negative and $\Delta G^\circ = -nFE^\circ$ ($E^\circ$ is standard cell potential).

So the $E^\circ$ value increases, and so does the concentration (because of backwards reaction), so the cell doesn't actually get charged up. 

Ideally just charge it by passing current in the other direction.