I never worry too much about my fish during a water change. I mean, I'm careful not to hit them or trap them with the gravel cleaner and I don't make sudden movements but in general I think they rather like the activity and enjoy getting a workout and putting their shoaling behaviors to work.
Heaters are not, in my experience, calibrated to match their rheostats to numerical temperature reality. They are meant to be used in conjunction with a thermometer. Often they have a procedure, sometimes in their user manual, allowing you to adjust the numeric dial separately from the actual rheostat knob to make the numbers match reality.
For instance, on some, once you determine the temperature is at a particular value with your thermometer, you pull the knob gently outward and rotate it so that the correct number lines up with the pointer and then let it back in. From then on the numbers on the heater dial will match what the thermometer is saying. The heater should also be right at the point of its pilot light coming on when you do this, rather than in a range where the light would be on continuously or off continuously.
~~waterdrop~~