That's a pretty big space, 500 watts won't overheat the area. I use 250 watt heat lamps but my enclosures were smaller. I put an insulated lid on top and wrapped with plastic and the the temp gain was about 15*. This was last year. Those structures were about 7' tall and 5' wide. Depending on how you insulate it, will determine how much heat it will hold.
The forcasts went crazy for Monday morning the last couple days. I mostly follow AccuWeather and they went from 40* to 32* for my area and held it about 24 hours then yesterday it went to 27* so I went into prepping mode. By late afternoon the forcasts bounced all the way up to 40* and this morning it says 43*. I think we will be ok for now but the very end of January early February is looking like we will get hit. The AO is forcasts to drop big time and the NAO is moving down into the negative as well which is bad. The PNA has been positive (which is bad for us if you want to avoid cold), and looks to remain positive so with these three all going in a bad direction near the end of the month I expect some freeze shots will be coming, at least for my area in Lakeland.