Yes it willWith a thermostat you are taking the probe and taping it to the heat tape. Well this is outside the tubs, so your thermostat is not adjusting with the temp inside the tubs. It seems like once the Heat tape hits the certain temp you are looking for, its not going to adjust at all since your probe is taped to the flexwatt.For instance if your house temp goes up and down 6-8 degrees your helix will prob not recognize this change since its taped to the heat tape and not inside the tub.
A reliable thermostat such has Helix or Herpstat will adjust the temps constantly to maintain proper temps.
A rheostat will not adjust the temps and let the temps fluctuate greatly. If the ambient temp of your room fluctuates the temps will fall and rise all the time and you will need to adjust your rheostat all the time.
If the temp rises in your room this could lead to a temp spike on the warm side and you want to avoid that.
Spending money on a reliable thermostat will be money well spent.