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So long story short, my buddy wants me to build him some prototype that uses an Arduino board and a temperature sensor to control a heating element. Basically, a thermostat. He'd like *some* interface (text, maybe an app/BT connection) to set the desired temperature. If the sensor reads above, switch off. If it reads below, switch on. Easy enough.
This would be my first crack at an Arduino project. I have a BS in CS, haven't coded in a long time, but I'm not worried about being able to shake the rust off there. Where my ignorance gets the best of me is the hardware. My buddy tends to have a short attention span, so I don't feel like dropping texa$ on his little experiment. That being said I'd like to do it just as a hobby type thing, even if his interest wanes.
So the question is this; Is there any particular Arduino board that would meet the above requirements yet still be in the $10-15 USD range?