If it stays on all night in a warm room it will keep rising (not a clue to what temp tho'), use a timer plug and set it to come on every half an hour for 10mins or whatever suits the ambient temp of the room.
You might be best using an inkbird (or cheap knock off) temp controller. I use a heat belt sometimes but never without temp control.
There's a Chinese one around on eBay/Amazon for around a tenner with 1 plug socket. It does the job, or if you are ok.with electrics you can get stc1000s for a few quid.
Keep clear of the orange rubber chinese heat belts .They are death traps badly wired and get so hot they would melt plastic !!! Ordered one threw it away .Once I had sorted the wiring plugged it in and with 5 mins was so hot it burnt my finger bigtime .Supplier obviously knows this. He said he would give me my money back as long as I didn't leave negative feedback on ebay