Controlling and powering a heating element, thermometer, and screen.

Something like this can help you control a 120 AC device If your unfamiliar with high voltage.

I've seen a DIY incubators use a low watt light bulb to produce enough heat for chickens, unless your looking to build something a large. In which case, if you are familiar with household wiring, a light bulb and an incandescent bulb pigtail like this would be easily wired up to a relay like this...

The relay kit from sparkfun