PURPOSE: To obtain a controlling device of an air heater which is aimed at preventing corrosion and also improving a heat efficiency.

CONSTITUTION: An air heater 2, a waste gas temperature detecting device 16 and a sulfuric acid dew point temperature detecting device 11 provided at an outlet part of a combustion waste gas of the air heater, an arithmetic unit 12 receiving an output of each of these devices and calculating a set value of a prescribed low outlet temperature in a range wherein the part of the air heater tending to corrode does not form dew, and a temperature controller 13 receiving outputs of the arithmetic unit and the waste gas temperature detecting device and delivering to a speed changing device 14 such a control signal as to make the output of the waste gas temperature detecting device be the set value of the outlet temperature, are provided.