I did some searching and can't find an exact answer to why to use hot water?
I read about doing roofs in cold weather and see the possible assistance that may help out with, but is it usually used in conjunction with TSP only. Not thinking I'm gonna need to use TSP in my mixture.
Yes it helps TSP dilute into solution. It will help tremendously in cold weather and honestly will probably clean better most of the time. But it is not necessary at all. If you want to clean lots of concrete than hot water is for you. It will always help you mix any cleaning powders for any solutions easier, as well as make house washing and other cleaning tasks go faster. I would just try a cold water rig for now and see if the hot water is something you want, as it is expensive to buy a ho****er mobile unit and is easy to add in the future.