Nah, as one that has personally taken 12,000 VAC in a lake (Shasta to be exact), house current in a bath tub is just a tickle, sort of a good wake-you-up after you've seen one to many pop-ups for p0rn. But, I do disagree, it will not cool off the powersupply, at least not immediately, and certainly not as well as simply unplugging the bugger would and you avoid all that flash and glare that is so tedious on tender eyes. I mean, why are you taking that nice hot bath for anyway? Simply won't do to create all that hub-bub.
Frankly, unless you have the psu down your pants or in a similarly familiar location, what do you care how hot it gets, as long as it doesn't start a fire. That's typically around 456 F (235 C). Keep it well ventilated and it should be just fine.