The temp will be stable for a long time, days. It takes a lot of thermal energy to warm up all that water and beer. Especially if you are only trying to maintain 65 in a house that's close to 70.
get the water down to the temp you want it, and it'll start right around there very easily. I get mine down to the low 60s or high 50s depending on the yeast/beer, then it just takes two gallon jugs of ice set over for me to maintain that temp for days at a time.