Cooling controller and control method for cooling device

A cooling device includes an inner passage, an outer passage, an engine-driven pump, an electromagnetic control valve, and a driving circuit that regulates current flowing through the electromagnetic control valve by activating and deactivating a switching element. A cooling controller for the cooling device includes a processing circuit configured to execute an operation process for operating, when the engine-driven pump is driven, the switching element by setting a duty cycle of an activation time to a switching cycle, which is a reciprocal of a switching frequency of the switching element, to be a larger value when a temperature of the internal combustion engine is low than when the temperature is high and a cycle varying process for setting a longer switching cycle when the temperature of the internal combustion engine is less than a preset temperature than when the temperature is greater than or equal to the preset temperature.