degree difference from outside to inside grow room

Riu, the forecast here says 31 tonight. I am not running any heat in my house. So if its going to be 31, I can expect inside grow room temps to be around 45 degrees(my guess)?

45 is way too cold. There are a lot a variables to guess at that. How big is your space? Is it in a closet, garage, room etc.? Lights, ventilation etc...

Just pick up a space heater and put it on a low setting (if there is somewhere safe to put it). You could also turn down the ventilation if you have a fan controller.

Depending on your light wattage, 12-17 degrees difference is normal up to 600W, depending on room size.