I believe the cold baths are a factor in my improving tolerance for fasting but I’ve been changing many things and it is hard to attribute the relative importance of each. For many years I was losing my tolerance for both cold and heat and only able to comfortably function in an increasingly narrow range of temperature. I developed Raynaud’s syndrome, a severe loss of circulation to the hands and feet when chilled. And I was prone to fatigue, weakness and dizziness in heat. This improved when I went LCHF and then keto. But would flare when fasting and would make me end fasts on the 2nd or 3rd day.
I started doing thermal stress via hot and cold baths because it can stimulate growth of new mitochondria in both fat and muscle and I hoped it might improve my tolerance for temperature variations. I had to start somewhat gradually because cold baths made my blood pressure spike and hot baths made my blood pressure crash, my pulse race and would make me feel faint.
Improved tolerance for heat & cold didn’t happen right away and it is was so horribly unpleasant getting into the cold water that I probably would have stopped after the first time, except I experienced a couple strong benefits right away. First I had several chronic pains and after the cold bath they were gone - gradually came back over a few hours but still the relief was unexpected and outweighed the couple minutes of extreme unpleasantness after first getting in the water. And after getting out I felt energized. This is a bit variable, sometimes it is amazing and other times not so much and once in a while I over do it and I end up feeling chilled and run down - mostly only if I’m already sick or very fatigued, also have to be careful when fasted for several days not to over do it.
The hot baths are much less unpleasant to enter and easier to do though perhaps more dangerous - fainting in hot water would be bad. But I also experienced immediate benefits. I found that a hot bath before going to bed promoted much better sleep and sleeping better resulted in many other improvements.