if the temps in the tub is that much higher than the herpstat setting, and the room temp isn't too high either you're way of measuring the temps is off. you kind of ruled that out with also using a temp gun and getting very close readings with both. then getting higher temps than what the thermostat is set at is most likely a bad reading on the probe. most likely how and where's it's mounted. mine is metal taped to the heat tape where the tub can no way knock it loose or off. if you check these, then you need to call spyder robotics
never place the probe in the tub. if the snake knocks it loose, you can get a hotspot that can burn your snake.