Short answer-
RTFM!
Kidding- but yeah, the manual is best, although technical. Try
googling A419 thermostat- the A419 is used by beer abusers, snake growing weirdos, greenhouse operators, and every store and bar.
I have a thermostat controlled exhaust fan in my greenhouse. I also have a normal box fan that's up high blowing air down, circulating the hot air down. The box fan is on a timer so it comes on during the day, shuts off at night.
The thermostat used to control the exhaust fan appears to me to be a standard household thermostat, intended for electrical HVAC (I'm not at home at the moment so I don't have the make or model number). The exhaust fan is in the peak, and it has louvers to keep it sealed when not in use. I don't know the exact dimensions on the fan itself but I'm pretty sure it's a 12". A couple days ago, with the exhaust fan turned off and full sun on the greenhouse, I had 120°F while ambient outside was 39°F. I turned on the exhaust fan, with the thermostat set to 70°F. Within 30 minutes the thermometer was reading 70°F. A 12" fan will totally exchange all air in a small greenhouse literally within a matter of minutes, and will bring a greenhouse down to ambient temperature.
I would recommend a
Johnson Controls A419 digital thermostat. They are cheap, programmable for both range and span, they have a remote thermoprobe for more accurate temperature reading, and super easy to wire up into ANYTHING, either for heating or for cooling. I also have one on my kegerator
You could poorboy it and try to score an old/cheap/free/maybe still working electrical home thermostat like what I've currently got, but I wouldn't recommend it. Do it right, do it once, don't burn down the house.
I would also recommend a standard 10" or 12" industrial exhaust fan- they come pre-mounted into a frame that contains the louvers, and they're extremely easy to install. Wire the thermostat inline and you're done.
About $55 for the A419 and I bet you could pick up a 10" or 12" locally for about $100-$150. Expensive I know, but it is definitely the one part of a greenhouse you need to spend money on- one hot day can kill everything.