Scored a Freezer for Fermentation

So I've been scouring craigslist for a chest freezer to use for fermentation and I finally scored one the other day for $50. Now the only question I have is not about what to buy, but about the controllers themselves. If I use a johnson or ranco controller like this one, and let's say I have a setpoint of 67 F and a differential of +/- 5 F, what will happen if the ambient temperature drops below 62 F, will it give power to the freezer or will I be able to turn that feature off so that it only will give power to the freezer when it goes above 67 F and not below?

The reason I'm asking this is because I'm going to keep my fermentation chamber in my garage, and I don't know how cold it actually gets out there during the colder months. We had a pretty mild winter last year, and my guess is that it's not going to get much colder here next year either, but for all intensive purposes, if I'm away and it does get cold, I don't want my freezer to do what it's supposed to do and freeze my beer.

It should only be set to cut ON at (Setpoint + dif). This is done by config'ing jumpers inside the units. The Johnson A419 (very popular) allows you to change all these settings.

I have mine set to 41F +/- 3F. It usually drops to 38 at lowest, and does just fine. It shouldn't be switching ON for being UNDER temp unless you're using a heating setup.

Thanks for the reply, but instead I bought a STC-1000 off of ebay, this way I'll be able to hook up a heating element along with the freezer and I'll be able to run it in the winter, lagering, aleing in the summer, (not sure if that's a real word). The freezer is a kenmore and it runs at 5 amps x 115 volts, I don't think I'll need a relay so I don't burn out the STC-1000, but someone with better electrical knowledge may be able to chime in.