I wouldn't worry too much about heat in them for just a few hrs. A few times I forgot to replug in my heater on my 29 gallon(after a water change) that had african mbuna in it and it was around 67 degrees F for a day or so

. They will 'slow down' and become less active, which might be good for them when they're in buckets. I've never lost any fish...thank God! So i imagine that for a little while, it should be alright!
Like ACE said have a bucket to put your filter in/or keep your filter in tank water...depending on which type you have you'll keep it wet in different ways.
OH YEA.....make sure any bucket you use is CLEAN!!! Rinse, rinse and rinse again if it's ever had anything in that's bad for fish.....otherwise contaminants from the bucket could kill your fish.
I would start the project early in the morning...clean the tank hopefully by at least 12 noon. Then fill it back up w/water using the declorinator and I'd let it sit for a little while, few hours. The declorinator pretty much instantly declorinates, but it's a good idea to let it sit for a bit. (Some people need to do 90% water changes in some cases with fin in and they end up fine.)
If you do it w/in about 6-8 hours, I'd say you wouldn't need to cycle the tank. Although, you may have a mini cycle depending on how your bacteria holds up in your filter. If you get a mini cycle make sure to do water changes to keep ammonia and nitrite levels at or below .25ppm....if you don't have a liquid test kit, then get 1!! I wouldn't think that the mini cycle would last very long.
One more thing. Make sure the temp of the water you're putting in the tank is about the same as what's in the buckets. Then when you add the fish back in, they won't get a temp shock! After the fish are back in, put the heaters in and it'll start gradually warming back up and your fish will start becoming more active.