When I was using a plastic tub I got the same result. The thicker the plastic the better. I used a flimsy one as well, and go the same result. Definitely not because of how hot it was(the mat itself was even set to 28 degrees and it still did this) The heat mat was also temperature regulated, and I had half an inch of airflow between the plastic and heat mat, and then one inch between the heat mat to the table top. It didn’t warp significantly, but I found that the bottom on one side would cave in slightly(similar to when you put too much weight onto a plastic lid and it bends slightly) Just make sure your tub is made of sturdier/thicker plastic.
If the change is significant, or if certain spots of the bottom of the container is thinner, than that would mean your heat mat is either too hot, or too close to the plastic.
Also, 93 is the maximum it should be, so if your temperature controller fluctuates a degree or 2 up or down, then I would set it to a degree or two lower.