You can measure the height of a room using a thermometer only if
a) you know the relation between height and temperature
b) the thermometer is of sufficient accuracy.
A thermometer measures temperature. If there is no relation between height and temperature, then you cannot measure height using a thermometer.
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On the other hand, you could use the thermometer as a ruler (or trade it for a method of determining room height). You could say, "the height of the room is 23 times the length of my thermometer," for example.
a) you know the relation between height and temperature
b) the thermometer is of sufficient accuracy.
A thermometer measures temperature. If there is no relation between height and temperature, then you cannot measure height using a thermometer.
_____
On the other hand, you could use the thermometer as a ruler (or trade it for a method of determining room height). You could say, "the height of the room is 23 times the length of my thermometer," for example.