i did a water chang in my tank the other day also. but i had the same concern. so about 5 or so hours before i did my change, i stuck the heater from my tank into the bucket of water that i planned on putting into the tank. it warmed the water in the bucket up to the same temp of the tank.
haven't gotten the new thermometor yet. Money is a little tight so I am gonna have to hold off on that for a while. Stuck with the little strip on the outside for now
PS I know they are pretty cheap but I am setting up a ten gallon hospital tank so I need every cent