Ok, I played around with the wiring and thermostat, and here is what happened:

This is the thermistor in the thermostat, I just desoldered the joints and pulled it out

I wired some 24 guage wire into where the thermistor was

and attached the thermistor on the other end of the wires. I had to play around with it a bit to get the polarity right so the thermostat would work, but other than this, and having very little soldering experience, this wasn't too bad