I think that the metal and trace elements found in tap water is the drive behind using RO units and I admit that I started out being the skeptic and only used tap water in my tank but later I changed to RO and there is a difference in the speed of algea growth, how often my skimmer needs to be emptied, and (I think, but my wife doesnt) more colorful fish.
I cure my water in my basement in a garbage can and like you said, who knows how much the water cools as I am carrying it across the house. Still, I dont think it is all that much and there is the ambient temp thing that states the water will only cool or warm up to be equal to the temp in the room it is in.
Anyways, I just bought myself a 500 gph submerable pump for about 30 dollars and a long peice of clear hose from the hardware store. I use the pump to airate my water and mix in the salt, with a heater in the garbage can to equalize the temp between that water and my tank. I then just use a hose clamp to attach the tubing to the pump and shazam! the water is in the tank without me breaking my back or having to worry about temps. Then again, I also have a semi-large tank and change about 30 gallons of water every other week.