It's not a matter of the overnight temp, it's a matter of whether or not A/C is in use where you'll be sleeping. I keep my house thermostat at 76*F but I have to be cognizant of where the air ducts are as the cooled air comes out around 60-65*F - you don't want your BP sitting by that all night.
Should I buy a hand warmer or something to put under his tub (with a few towels in between as a buffer)?