My Weller temperature-controlled soldering iron uses a very inexpensive method. It has a magnet in its heating element that loses its magnetism when it reaches the "Curie Point" temperature. The magnet pulls a switch to turn on the power to the tip and a spring turns it off when it reaches the Curie temperature. It turns on and off all the time.
I don't know why different tips provide selectable different temperatures.
Some people do soldering in the very dry air of a desert (Arizona?) so a damp sponge will dry out very quickly and will be a nuisance to keep it wet. They should use brass curls.