Everyone else has given you some good ideas. As far as kidneys controlling your body temperature, that makes sense - my usual body temperature fluctuates between 96.5 and 97.8 these days. I don't think it goes up after dialysis, but I've never checked it myself with the same thermometer right afterward. Later in the night on D days, it's not high.
One thing that I wonder about: when I was on PD, everything was labeled with "non-pyrogenic," that is, not fever-causing. Are some dialyzers not non-pyrogenic? Or, if dialyzers are reused, could something in the detergent or some other factor cause a transient fever?
That hot flash when your BP drops is part of the adrenergic response - adrenaline. It's a multi-purpose reaction; it increases your heart rate, constricts blood vessels, and a few other things, including a hot flash (blood rushing to your skin) and sweating, both meant to quickly cool you down, useful in the fight or flight response. (Yay physiology class!
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The only other thing I can think of (which I expect they would have already checked) - are they giving you iron when you're on dialysis? I've had reactions to IV infusions of Venofer, and it's possible a mild reaction could increase your temperature, but it's just a guess.
I hope you figure this out. It can't be good to have a fever higher than 101 three times a week. What if you take some Tylenol after you get off?