Based on your wording It sounds like you want to run the cool side off just a dimmer and the hot side off a thermostat. What I would do personally if I were in your shoes is use the one thermostat for both sides but put the dimmer in the cool side. Basically the johnson turns both hot and cool sides on and off at the same time but because you have the dimmer on the cool side it dosn't get as hot.. It is safer than just relying on the dimmer alone.
I hope that made some sense..
Richard