I would leave the mat on 24/7, but to know what your temps are before starting, I would check the mix temperature after 24 hours. The temperature of the room air will have some effect on the mix temperature too so I assume that temperature is fairly constant. Even though you think the plastic cover is air tight, I think you will find with the heat the water will evaporate faster than you expect. Al

I've looked at it twice now, but have not checked the temperature. I will have to see what thermometer I have that can fit inside the flat. It feels very cozy! Like my bathroom after a shower.

There is much condensation on the plastic lid, but I'd expect that anyway even without the heat. I guess I'm seeing at as a potential rot situation with that lid on there.

Plants thrive by being given a specific time of growing, then they should be given a 'rest'.
Forcing a plant to grow 24/7 would be like putting yourself on a steady diet of food and sunlight.
You wouldn't like it, neither does a plant. It must have a rest.
Usually the seed or seedling is given up to 16 hours of growth phase, then 8 hours of rest.
Time your growth phase with a timer.
Water only as the plant requires to keep it damp...no more.

My incubator I use for my tropical plants will hold 8 one gallon nursery pots. Right now I am starting my Tuberose bulbs 8 at a time. By starting them at 85 degrees for a week they will grow to about 4 inches, then I take them out and keep them in the coldframe, while starting another 8 gallons. This gets them off to such a great start they will all bloom before the weather cools in the fall. Of course I prefer they grow than rest. Al

Can anyone tell me if you take the caladium tubers off the heat mat when they sprout (like you would seeds)?

Yes. The Heat mat is only used to wake them from dormancy. Once they sprout I take them off.