A controller for an inhalation device, comprising: a power supplier configured to supply power to a heater used to heat and atomize an aerosol source; a detection circuit configured to detect a resistance value (R HTR) of the heater; and a processor configured to execute heating processing of heating the aerosol source by controlling the power supplier to supply the power to the heater in accordance with reception of an atomization request of the aerosol source, wherein the processor controls the heating processing based on the resistance value (R HTR) of the heater detected using the detection circuit during the heating processing, a reference temperature of the heater, and a reference resistance value of the heater at the reference temperature, wherein the processor performs cooling determination processing of determining whether natural cooling of the heater is completed after the end of the heating processing according to reception of the atomization request, detects a resistance value (R HTR) of the heater using the detection circuit in a case of determining that the natural cooling is completed in the cooling determination processing, and updates the reference resistance value by the resistance value (R HTR) of the heater detected using the detection circuit after an end of the heating processing and before the reception of the next atomization request, and characterized in that in the cooling determination processing, the processor starts monitoring a temporal change ratio of the resistance value (R HTR) of the heater detected using the detection circuit after the end of the heating processing, and determines that the natural cooling of the heater is completed, in a case where the temporal change ratio falls within an allowable range. a power supplier configured to supply power to a heater used to heat and atomize an aerosol source; a detection circuit configured to detect a resistance value (R HTR) of the heater; and a processor configured to execute heating processing of heating the aerosol source by controlling the power supplier to supply the power to the heater in accordance with reception of an atomization request of the aerosol source, wherein the processor controls the heating processing based on the resistance value (R HTR) of the heater detected using the detection circuit during the heating processing, a reference temperature of the heater, and a reference resistance value of the heater at the reference temperature, wherein the processor performs cooling determination processing of determining whether natural cooling of the heater is completed after the end of the heating processing according to reception of the atomization request, detects a resistance value (R HTR) of the heater using the detection circuit in a case of determining that the natural cooling is completed in the cooling determination processing, and updates the reference resistance value by the resistance value (R HTR) of the heater detected using the detection circuit after an end of the heating processing and before the reception of the next atomization request, and performs cooling determination processing of determining whether natural cooling of the heater is completed after the end of the heating processing according to reception of the atomization request, detects a resistance value (R HTR) of the heater using the detection circuit in a case of determining that the natural cooling is completed in the cooling determination processing, and updates the reference resistance value by the resistance value (R HTR) of the heater detected using the detection circuit after an end of the heating processing and before the reception of the next atomization request, and characterized in that in the cooling determination processing, the processor starts monitoring a temporal change ratio of the resistance value (R HTR) of the heater detected using the detection circuit after the end of the heating processing, and determines that the natural cooling of the heater is completed, in a case where the temporal change ratio falls within an allowable range.