Holy moly, I would say something is wrong. If you are using a thermostat/rheostat, which I'm guessing you are if your temps aren't reading well over 100? If you are using a cheap thermostat it's definitely possible that it's not doing a good job keeping control of the temps, but I'm still not totally sure it would burn/melt your plastic. The melting point of most plastics is well over 200 degrees-that's why plastic dishes/tupperware doesn't melt in the microwave when you boil soup and other liquids.
Is it possible that your elements are exposed? I'm wondering if that's what happening since you have burning. I use really cheap tubs, we're talking 98 cents for the hatchlings and I've never had that happen. I also use those tubs over human heat pads to warm up f/t rats. My human heat pad gets up to 160+ at the hottest setting, if you put it on your skin you'll get a first degree burn! I've never had tubs burn or melt at that temp. The burning makes me think there is electrical issues, when you solder, 500+ degrees, the plastic doesn't burn, it melts.