As mentioned, you definitely do not want to use household softened water in your aquarium as the salt typically used to soften water is very bad for fish.
Having 'said' this, there are a number of ways to warm your outside, unsoftened hose water.
I found that Wallymart sells 'Primo' water in 5g bottles for $11. (since bottled water costs about $1 a gallon, the bottle is costing $6 which makes it a good deal.
You can get and keep two or three of these bottles and (as 1077 wrote) fill with your hose and warm these to room temperature. With summer, you might warm in the sun. I go a step further and have inexpensive Tetra submersible heaters (2-15g) that I drop in the night before the water change.
(Alternatively you can get 5g pails w/lids from a big box store.)
You could use a larger container a bucket dip for the changes, but don't plan too far ahead unless you circulate or aerate the water as stagnant, open water develops a nasty slime.