IMO the volume of beer you are dealing with will not change temperatures as quickly as you think.
Do you have a fermometer stuck on the side of the vessel? What temperature is it reading as that should be pretty close to what is in the vessel.
One thing to keep in mind is that active fermentation can raise the temperature inside the vessel anywhere from 5-10 degrees so keep an eye on what's going on. Stability with temperatures is most important during active fermentation as that is when the most off flavors can be produced by the yeast.
You might want to consider placing the vessel in a bucket of water-swamp cooler-this will provide insulation from the temperature swings in the house