Yes, but it looks like if you do it at home, some of the shots develop upside down!!! That could be a real problem when viewing them! Some of us are getting too old to stand on our heads anymore!!! LoL LoL SS
I processed color negative film in C-41 for several years for a very small mom-and-pop publishing company. This was back in the '80's. I built my own processing system using Patterson 8-reel tanks and constructed temperature water baths from large Rubbermaid tubs (available at Wal-Mart). I lined the tubs on the outside with household insulation. Once I got the water bath up to the desired temp, I found that it would keep the desired temp steady all the way through the developing process. This system worked for a couple of years. It was primitive, but it worked and I got good and predictible results. Later, I would use the same system to develop Ektachrome in E6 chemistry. It worked just as well for that, too.
Just for fun I tried a three solution Tetinal (brand name) kit. As others have mentioned, keeping the correct temperature of the solution and keeping temps stable while in with the film in the developing tanks was very important but not overly difficult. The kits were pricey, they are good for I think around 10 rolls, store guy said some get more. biggest problem was that once mixed, the solutions have a limited shelf life so to make the most of it one would have to shoot at least 10 - 12 rolls then have the time to develop them over no more than two days, one day being better. I don't shoot colour film as a rule and if I do in future will most likely search out a reputable lab.
I used to do color film at home when I was a student, and poor. I used a Unicolor kit. I made a "water jacket" from an electric frying pan. I then meticulously adjusted the water from the tap, then prayed nobody flushed the toilet or took a shower. I got good results. Danny
Honestly, processing C-41 process film is really not that difficult but it is more critical than B&W when it comes to temperature. I built a thermostatically controlled water bath to keep the chemistries ±1/2ºF but it is possible do the same manually. Get a deep tub and fill it with water at the temperature you will be using. Stick an accurate and calibrated darkroom thermometer into the water and add hot water as needed to maintain the temperature. You could also try using an aquarium heater but I have found that they are not particularly repeatable and you need a small submersible pump to keep the water evenly mixed. I did this for many years with great success. Modern day C-41 chemistries have a wider temp latitude (most are ±1/2ºF) than the ones I first started with, which were usually ±1/4ºF which was pretty difficult to maintain.