C-41 processing can be done with the same equipment you use for B&W film, although you will need to do it at a higher temperature (100F). This makes a water bath a practical necessity if you're using manual tanks or the like for film processing. Heated processing equipment is another way to go, but a much pricier one. If you're developing C-41 sheet film in trays, you'll need to keep the trays at 100F. I've not done this myself (I use 35mm and MF film), but I'd think a water bath would work for that, too; or maybe you could use heated pads.
For making prints, temperature is less critical. I do RA-4 at room temperature, which ranges from 68F (20C) to 90F (32C) in my darkroom. (I have no central A/C.) I develop a little longer at cooler temperatures, and it's possible my filtration varies a bit. (I've not looked into this in detail.) Personally, I prefer doing RA-4 in open trays, just like B&W, but I get the impression that most people prefer drums because drums can be used in room light, much like film tanks.
My experience is that C-41 and RA-4 developers last for months in stock form, but they go bad pretty quickly (in a few days) at working strength. C-41 bleach lasts a very long time, and C-41 fixer is much like most B&W fixers; it lasts weeks or months. RA-4 blix, by its nature, is unstable. I'm not sure how long it lasts, but I try to use it within two or three days of mixing it. Given all this, I wouldn't worry about cold-storing your film before processing it, at least not from an economic point of view. Just dilute enough developer to handle whatever you're processing and go at it. (I use C-41 one-shot, although some people re-use it once or twice.) The remaining stock solution developer, if fresh, will keep for months; the bleach will keep for even longer; and any diluted but unused fixer will keep for a few weeks.