heres how i do it-
1-fill the filter directly from my sink. put the filter on the counter while the water goes through the media. it takes like 1/2 hour, for the top to be completely filtered, but as the level in the top lowers i keep topping it off and emptying the bottom (filtered) water into a bucket untill i have enough.
2-i leave the bucket with the filtered water overnight with an airstone in it. if im adding salt for a change i do this before the airstone. i add it, stir it in, and then aerate.
3- i dont have an extra heater, its in my QT, but i guess at this point you should try to get the temp as close as possible to the temp of your tank. but i add mine cold, straight into the aquarium, sometimes with stress coat (wich helps slime coat but is irrelevant right now.) just like a regular water change.