iOS Bluetooth Automotive Dashboard via Uno - 12V on/off signal

Okay... another dumb idea. I have a thermocoupler. When the temperature gets to a set level, it goes to ground, which closes a relay that turns on the fan. What if I have a digital pin pulled up, and when that thermo coupler goes to ground, it pulls it down? So HIGH would be off, and LOW would be on? No level shifting. Probably an external resistor just as a safety check against over-drawing.

That should work right?