Whatever you do, do not soak your tort under a heat lamp. I have personally overheated my tortoise this way. I now just dump the cooler water out and refill with warmer water.
I play musical pails: 2 torts and 3 pails. Because they always eliminate in their water, I move the 1st tort that finishes their business into a fresh warm water. Usually, by the time I'm finished washing the 1st pail, the 2nd tort is just finishing their business, so they go into fresh warm water.
Try insulating under the pan to keep the direct heat transfer to a minimum. In winter, I put a 1" thick sheet of foam under my soaking tub. In summer I find the temperature stays warm enough during their 20 min soak.
You could also cover most of the tub to keep in the heat.
I soak mine partially in the sun. I watch them very closely and over time have developed a routine in a certain spot in my yard at a certain time of day. I have to keep shifting the soak tubs more into the sun. The water evaporates and cools, but the sun warms the part that it touches. Its a nice balance. If I forget them, they will end up in full shade and the water will cool, but with our summer days always in the mid 90's, this is still okay.
Indoors you can put a lid on the top, and that will greatly slow down the evaporation and rate of cooling.
I put the cleaned soaking pan in their closed chamber, filled with warm water to a proper tortoise level. It offers a large surface for evaporation in the chamber, and it is chamber temp. They soak while a prepare salads, get fresh food, and go about their day. I then clean the pan, refill it with warm water, and by the next day, when it is soak time the temp of the water is again chamber perfect.
I store their drinking water, plant water, etc. in a bottle in the chambers, so it is chamber temp.
I have never worried about the soaking water getting too cold. Normally the temperature inside my house is in the 70's. Soaking water won't get any colder than the room temperature. If your room is 75F degrees, that's not too cold for a soak.
Wow, great suggestions, everybody. I wonder if I'm expecting the water to stay too warm. Here's my routine: I usually soak outside when I get home from work and the air temps this time of year are 75-85 that time of day. My torts go in a mixing tub in the sun 2/3 covered by plywood. I like it cause they can decide if they want the sunny side or the shady side. I just judge the water using my hands, but after about 15 mins, it seems too cool to me. Maybe I'm being too particular. The torts usually scramble around regardless.
I fill the sink with super warm water (about 1 inch) and put the soaking tub on top of that. Then I fill THAT to my desired depth with warm water. I find that keeps it warmer a bit longer. I do find I have to change it out and some point. It does cool down. BUT he doesn't seem to mind it (well, he hates it when I have to wake him to change it...lol)