I'm not a fan of space heaters either - but I kept mine on all the time when I lived in Alaska. It's gets pretty freakin cold inside when it's -60F outside and you happen to live in a ghetto 70 yr old apartment
Depending on how cold it is where you are, I think I would either float the bettas with the goldies or if its not that cold, wrap the bettas tank in towels.
Not sure if a space heeater would be enough to keep them warm..I had a small little ceramic one, not the bigger kind with the exposed coils - those kinda scare me. I was afraid those would start a fire when I was asleep