Another stupid question from me!

Even with a 75-watt infared heat lamp (approx. 4 inches away from the tub's cool side, cannot get any closer), my cool side still drops to about 76 ºF at night. If the room temperature gets below 78 or so, the cool side dips below its normal range of 81-82. This will start to be a problem in the next few weeks as it's nearing winter and the room temperature drops to 68 or lower, thus making an RI almost guaranteed to happen unless I do something about it. I know a simple solution would be to just get another UTH, but I don't want to go that route as I would have to get another thermostat, etc., and I'd need a bigger one when he was an adult (I'll be needing a bigger warm side UTH when he's bigger anyway), so a space heater seems like a logical way to go.

Okay, now the questions. I'm thinking about this one.
1) Can space heaters like that be left on 24/7?
2) How much would that cost electricity-wise?
3) Does the thermostat keep the room at the set temperature all the time (unless of course it gets hotter than the selected temperature), or is it just an approximate setting that will fluctuate some?
4) Is 80 okay to set the thermostat to? What is acceptable? I haven't really experimented if the tub keeps the cool side any warmer than the ambient room temperature, as I've been using the spare 75-watt bulb. I'm using a 27 qt. tub with 50 airholes; 16 on each long side, 9 on each short side. The UTH covers a small amount less than half of the tub.

Thanks a bunch in advance. It's very helpful.