Galvanic cell: where does the temperature increase?

[Ran]

In which part of a galvanic cell does the temperature increase, if nothing is attached to use up the electrical energy (other than wire resistance)?

 

I am considering a construction of a galvanic cell like this:

http://chemwiki.ucdavis.edu/@api/deki/files/6149/=ZnCu_detail.gif

 

I assume that a galvanic cell without a load will work just like any exothermic reaction. So where does it get warmer? Is it in both the anode and the cathode electroytes? Or is it only the cathode electrolyte that gets warmer? Maybe the anode will even cool down, since energy is required to release electrons from the anode.