Wow, 98?! Sounds like you're gonna have some creative fun!
I know, I was just joking.
I didn't even know they made bathtubs like that. Shows ya how long its been since I've had a baby. None of my friends have even had babies that I could shop for recently.
As far as your bedroom being too cold for the baby, I wouldn't worry about that too much. Babies like to have lots of nice warm clothes on and be wrapped up tight in their blankets. Just take him to another room for changing time.
And yes, the ear thermometers are much easier. They also make pacifiers with thermometers on them, but I don't know how well they could possibly work. I've always been taught that you have to hold the thermometer under your tongue to get an accurate reading. Obviously a pacifier does not go under baby's tongue.

And babies do not like to have things up their butts any more than anyone else does, so that makes a rectal thermometer a pain in the butt...literally.
Of course!
Yeppers, that will work. You can't do any damage doing that and it is real easy to put it back.
I lost it a long time ago.