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I think it's as simple as two pairs of contacts: one pair heats, the other cools. At it's simplest, a thermostat turns on the heat when it's cold and the AC when it's hot. With a thermistor and a relay you should have all the hardware you need.
The fun part comes from writing software that regulates the temperature best and most efficiently (probably trickier than it seems). Then you add scheduling software and a net connection so you can control it remotely.
You would actually learn a lot from writing the temperature control algorithm about real world control. It's very easy to write something that oscillates wildly :-)
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