Suggestions for extensions.... (related)
If you added a real time clock, you could build in auto=setbacks to turn heating down for while you are at work, or the wee hours of the night.
If you have a burglar alarm, you could have an "alarm set" output from that feed an input on the thermostat to turn the heat down when you are away from home.
For anyone playing with such devices in a region where it gets cold enough to freeze pipes, you might want to consider wiring a traditional thermostat, set to about 45 degrees F in parallel with your Arduino thermostat, so that if the latter fails, the former will turn the heat on for you before your pipes freeze...