Here's another vote for waiting on the water change. Do you know if you have ammonia in your tap water? As in from chloramine or just chlorine? Chlorine can be evaporated pretty quickly with agitation (splashing), but chloramine will need to be treated with a proper dechlor (another vote for Prime).
The only instance I would NOT wait is if you are cycling and have high ammonia/nitrIte levels. In that case the lesser of two evils is to do a water change. In this case I would fill up your container with HOT tap water. Then sit there and slosh it around until it gets to your tank temperature. You want to get as many bubbles as possible in the water (a cleaned wisk like you'd use to make scrambled eggs works great for aerating, but make sure there is NO detergent on it). Don't skimp on the mixing!
Then unplug your filter when you do the water change. Let the water sit with the filter off for 30-60 minutes before turning it back on. If you do these steps you will have little chance of killing off the beneficial bacteria in your filter.
But again, only if you are having ammonia/nitrIte issues!
HTH