Honestly I would leave him in the tub, his temps and humidity in it are fine, and it's easier to maintain than a tank. If you're worried about an RI you can leave his hot spot at 94*F and see if it makes a difference - though you may find that he avoids it, which is counter-productive. If that's the case try dropping it to 92*F.
I did see in reading your past posts that you've only had him for a month, and about two weeks ago he dumped his water and ended up laying in a sopping wet tub for a few hours. So, I hope you've gotten a (more or less) undumpable water bowl for him, either one that's very heavy or one with a wider base than top will work. And, since you've only had him for a few weeks, it's possible that the stress from moving to a new home triggered it.