You're going to have issues until you put the probe for the thermostat that controls the heat directly on the heat. You have to consider the fact that the plastic insulates and diffuses the heat. By the time it's hot enough for the probe (if it's inside the tub over the heat) to pick up the temperature that you want it it to be at, the thermostat is reading a much higher amount because that heat has had to travel through the plastic.
Then think about the many degrees of difference you're going to have as it cycles down and then back up because of that issue. Instead of the probe being able to keep the heat at one consistent temperature, it will constantly raise and lower the amount of power, or if it's an on/off thermostat it will be constantly be turning on and off with many degrees variance between because it has to pass through all that plastic..
Then it takes the plastic slightly longer to cool down even when the actual heat tape has cooled down a bit moreso, which means it will take longer to heat up again. Do you understand the issue here?
It's a dangerous issue, and a costly one considering the extra power being used to compensate for the heat being diffused through plastic before its probe picks up the proper temp and turns it off or cycles it down. This will also wear out your thermostat quicker..
I'm telling you, you need to put the thermostat probe DIRECTLY on the heat source. Then put a probe for a thermometer directly on the plastic inside the tub over the heat source. Set the thermostat to where it needs to be to maintain the internal hot spot that you require as being read by the thermometer probe inside the tub.
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