Along a thermometer every digit is higher than the one before it. So a cell three places from the bulb is at least 4, and a cell two places before the tip is at most 7.
Digits already on the thermometer tighten those limits: a 6 halfway along means every cell before it is below 6 and every cell after it above 6.
Worked examples
2 positions from real Thermo puzzles on this site, the familiar case first. Step through each one: the board lights what each step talks about, and the arrows show what rules what out.
A short thermometer
Follow the lit thermometer from its round bulb to its tip. The digits must rise along it.
A long thermometer
The longer the thermometer, the narrower each cell’s range: a five-cell thermometer’s bulb can only be 1 to 5.
Where it fits
EasyThermometer Range is an Easy technique: Easy Thermo puzzles are the first to need it.
The Thermo overview explains the rule and the levels.
Try it on an Easy Thermo puzzle. Next Step points it out when it is the move.