EDITED (different relay part number)
You'll need a power supply (wall wart) capable of switching the relay. You could use a 12V relay
and cheap power supply
. I know, that doesn't help make it cheap, but if you want a relay that could be controlled by the batteries in your thermostat, it'd cost another $25.
Here's something to consider with that project - you'll need (assuming you have a soldering iron and solder):
Relay - $7
Power supply - $6
Wire - ~$5 (I like to use short extension cords - they look professional and don't cost much)
Now you're up to $42, which is roughly the cost of a purpose-built temperature controller in the first place.
On the bright side, it looks like a fun project...