If it is on a thermostat, as long as there is no failure, it shouldn't be on enough to build heat to the point of melting. Also, if it can melt a tub, it is dangerous to the snake and that is your bigger problem.
From some quick searching, tubs made of polypropylene and polyethylene are most common from what I can tell (i.e. sterilite) and the melting points for those materials all appear to be well above 200 degrees F or even over 300F.
Sent from my SM-G950U using Tapatalk