Other options are keep the room warmer with an oil filled heater on a Tstat(that's what I do).

Some of my quarantines go into a setup that is a tub that's kept inside a larger cage. The larger cage is heated by a radiant heat panel mounted on the top and controlled by a Tstat on top of the tub.

Also as mentioned previously you just run the heat lamp outside over the tub but that method would probably be harder to control exact temps.