Fermentor Chamber Thermostat Questions!

Hey everyone, I've been looking around the forums and haven't been able to answer some of the questions that I have, I apologize if I just missed them.\

I plan on building a heated fermentation chamber out of an old broken fridge and want to use a light bulb to heat it since I have had good experience with this method in the past. However I would like to hook up a thermostat to it to control the temperature better. I think I have a good understanding of how to hook the thermostat to the lamp, it seems like I just have to wire it in like a switch.

My biggest question that I have is that I understand that it turns on when the temperature gets low but is there any risk of over heating. How much of a degree difference will there be before it shuts off.

Also can anyone recommend a thermostat to me or tell me what to look for. I was just going to get a standard house wall thermostat, will this work well? Are digital thermostats more accurate for this purpose then a dial thermostat?

Also I would like to keep this build as cheap as possible so to have more money for my grain budget.

Thanks for any help you guys can offer!!

I do this with a Ranco thermostat (to cool and heat), the wiring was simple. You can set the +- difference with it, I have mine set to 2 degrees. I reccomend using a ceramic reptile heater instead of a light bulb though, in case it burns out.