If you still have the box your herpstat came in, it might have come with a spare fuse. I thought mine did.
Also, don't get one fuse, get a few, just in case.
You probably had a surge of some kind that fried the fuse. Or it became overloaded.
As long as no one is digesting, a space heater will be fine for the night, or even room temp.
If they are digesting, then yes, definitely the space heater.