I dont bother to even check or adjust the temp of the "new" water going into the tank..
but it depends on how large your tank is, and how much water you are replacing.
If you have a 10 gallon tank are relpacing 50% of the water, adjusting the temp of the new would probably be a good idea..otherwise, dont bother.
(also..if you have a 10 gallon, consider upgrading!
10 gallon tanks are really too small for a stable environment..
If I were king of the universe, I would make 29 gallon tanks the absolute minimum allowed,
and even though im not king of the universe, IMO "goldfish bowls" should be illegal, and considered animal abuse..
but I digress..)
I have a 28 gallon tank, and I replace 5 gallons when I do a water change,
so thats about 20%..
I simply let the "new" water sit in a bucket for 24 hours, to dispell chlorine to to warm to room temp.
then I do the water change (siphon and all that)
then dump in the 5 gallons!
yes, its at "room temp" and is usually slightly cooler than the tank water,
(which I think I keep around 78 degrees..I havent checked the temp in years)
IMO, its "close enough" and the fish have never seemed to mind..
in fact, the angelfish love to swim in the stream of new water as I pour it in!
Scot