Errrr...so it's a one stage thermostat, meaning you can only either heat to OR cool to a set temp and not have it switch between two? And it will only switch a 12V circuit for a fan? Sounds to me like you need some kind of relay that works from the 12V "message" from the thermostat but activates a 120V device.
Frankly it's getting out of my knowledge base but you might have a hobby electronics store near you with some advice. I do not mean Radio Shack. You could have a look at Parts Express on line or just Google for info on this.
In the long run though you might want to consider a thermostat that is 2 stage and can operate 120V appliances. That way if you get a big enough temperature variation your sytem will take care of it for you. That's why I went 2 stage. I'm going to get a freezer for a fermentation cabinet. There's no way Herself would let me put it in the house. If I could I'd be all most guaranteed to only ever cool (especially for lagers) because I live in NV. but it's going in the garage where it can be 115 in the summer and drastically less in the winter. Maybe I'll never need to heat but with the controller I have I can. I'm covered!
This is the kind of thing I'm thinking about. I am NOT qualified to tell you this is the correct thing and is safe to use, but the guys at Parts Express are...