After trying keeping a constant 58°C (136.4°F) temperature with a gas stove I decided to do the same experimentation with a halogen stove. Halogen stoves usually benefit from a thermostat working together with a thermometer probe which should help regulating the temperature of the pan.
For this experiment I took the same pan used with the gas stove and poured 4 litres of the water pipe already at 43°C. It took me quiet long (approx 20 minutes) to reach a steady 58°C (136.4°F) temperature (I had to fight with ice cube and play with the thermostat). I probably can improve this time repeating the process several times. Anyway, as you can see on the graphic, since I reached 58°C (136.4°F) I switched the thermostat at 1 (minimum) and let the stove work on itself. I was moving the water often to make sure the water was evenly at 58°C (136.4°F).
The result was not so bad I maintained the temperature in the range from 58°C to 59°C almost doing nothing (just moving the water) for a period of 20 minutes (see on the graphic).
I summed up my comments in the table below. Next step will be a bain marie that a friend of mine borrowed me.