I worry about too much heat FAR MORE THAN I worry too much about cold. I aim for 80-90 degrees gradient roughly. It sometimes gets down as low as 75 on the cool side. It sometimes gets as high as 94 at the hot side (where the basking area is right under the lamp.)
If the power went out and it got down to 60, I would take precautions to keep them warm and not worry too much, as long as it wasn't sustained for too long that cold.
However, if a thermostat failed and the ambient temps got over 100 degrees, I would remove them to cool off at room temp, and I would be FREAKING OUT! Organ/brain damage due to high heat and the fact that they cannot regulate their temps by sweating and such, like us mammals can.