You don't need to leave your water to age for 24 hours. That was how it was done, when water only had chlorine in it, as an alternative to using conditioner, as the chlorine would evaporate over 24 hours. However, these days water is filled with all kinds of nasties, such as chloramines, which takes 2 weeks to go, and heavy metals, which never go. It's just another one of those practices that has been peverted through hear-say (much like most people thinking that cycling is running the tank for 24 hours).
Basically, Prime works instantly. I give my water a quick stir to help release any dissolved gases, but you can add the water to your tank the second you've added Prime.
As for temperature, I just add the water slowly enough that the fact mine is not quite as warm as my tank water doesn't make a difference. :)