Uro UnderEnclosure Hide

I keep two Geryi Uros in a 4 x 2 x 2 enclosure with nice, hot basking spot and a cooler side. I also built in a tunnel that goes through the floor on the cool side to an enclosed plastic container filled with substrate and sphagnum moss. I spray it down often so they can get some humidity if they want. This is all completely UNDERNEATH the enclosure, so there is not heat getting in there. They use it a lot, more now that the days are getting shorter and cooler. They absolutely know to come up top side to warm up when they want/need. Pretty cool if I do say so myself! My question is: Should I add an under tank heater to this underground hide or leave it unheated? I assume that Uro burrows in the wild get pretty cold in the winter at night. Is it the cold that leads them to brumate? I live in Julian, CA (up in the winter snow elevations), So I assume it is colder up here than in the Sahara desert in winter. I don't heat my house at night, so temperatures can get into the 30s. I can absolutely get some heat to the burrow/container. I had the foresight to build in a tempered glass support/floor that the container sits on, So I can easily slap a small UTH on it.

I can show some photos and instructions/diagrams for this DIY project if anyone is interested.