I have accumulated a fair amount of experience with this in the last couple years hosting parties. You're close.
* Under 80, most people don't want to swim.
* The momentary shock-cold feeling when you jump in goes away somewhere near 85.
* 90 degrees feels warm and comfortable, not hot. A bit high for swimming on a hot day but much less than that and most folks don't want to swim at night.
* Less than 100 degrees feels "cold" for a hot tub. 104 keeps everyone happy. Hot tubs definitely go higher than 104 (although might require some funky button-work to "unlock" the temperature).
* 110+ feels tingly, dip-in-slowly hot. You go in for a few minutes, then sit on the side for a few minutes, then dip back in, etc. You could sit with your lower half in the water for an hour as long as your upper half was exposed and you had cold water to drink. You'll sweat a lot.
If the above poster has a hot tub set at 116, I wouldn't want to pay his electric bill.