This doubt came to my mind while answering the following question:
Why does a voltaic cell not operate unless the two separate compartments are connected by an external circuit?
The answer seems to be that only on connecting the two halves of a Redox reaction via an external circuit, does one allow the electrons to be transferred from one species to another. And while the electrons move towards their goal (to a higher potential), they do work in the way (light a bulb or a motor or something).
Another way to view this process is that the free energy of the Redox reaction is used to do useful electrical work.
But then my brain started to wonder and there came up a question - what happens to all this energy when none of it is actually used to do electrical work, i.e, when the Redox reaction is let to occur spontaneously, where does all the free energy go? Does it get converted to heat, thus warming the solution? Or does it simply stay stored in the solution in some form?