There are building codes governing the clearances of combusables and stove stacks. Follow tomh advice regarding the AC switch mounted within a legal distance of the stack or stove. Those laws are designed to protect you from imagining a safe idea that results in a bad fire.
I really liked your idea and tom's reply. I am hoping to put together a similar plan for my place. You'll get higher efficiency staying off the stove since the fan won't turn on unless the room air is warmed, albeit not much, it'll be a little more efficient.
For another great idea, check out Automatic Zone Registers, heat registers that shut off in non-thermostat areas of the home when you know heat isn't demanded, also improving efficiency.