Nonlinear functions (table and map) of a temperature estimation model are corrected based on outputs from a temperature sensor. An electronic control system calculates, for a plant model constructed to calculate an estimated temperature value of the plant, an estimated temperature value using a correlation model between a first parameter regarding the plant and a second parameter regarding the plant model. This control system controls the temperature of the plant based on the calculated estimated temperature value of the plant. The control system also defines a plurality of functions (Wi) in a range of a plurality of the first parameters for the correlation model, calculates correction coefficients (Kli, Kci) that adjust the height of the plurality of functions based on the output of the temperature sensor and the calculated estimated temperature value of the plant, and corrects the correlation model by the plurality of functions (Wi) and correction coefficients (Kli, Kci).