Sorry, what you're talking about is a perpetual motion machine, which the laws of thermodynamics forbid. The AC will just have to work harder to get the extra heat added by the thermoelectric device back out, no free energy here.
Thanks. Never had a knowledge about thermodynamics. I just googled perpetual motion and the laws of thermodynamics. And yes, I agree that my comment above doesn't follow those laws. It's good to learn these new things. :-)