When doing an experiment ive had that same exact UTH burn carpet in my bedroom, not on fire, but it is crispy and black. I'll take a picture later. A dimmer is cheap, and it will get the heat mat to acceptable temperatures.
I like the idea of using a dimmer...
I will definitely spend $5 on a dimmer instead of $50 on a thermostat, And I will regulate the temperature using my Infrared thermometer to get it to a more acceptable level.