1. A temperature management system to perform temperature management on an electronics device, the system comprising: a detector configured to detect a temperature of a heat generator of the electronics device, power consumption of the electronics device, and an intake air temperature of the electronics device; a cooling device configured to cool the electronics device; and a processor configured to control a manipulated variable to be given to the cooling device so that the temperature of the heat generator becomes close to a target value, the processor: controls the manipulated variable of the cooling device for a corresponding one of a plurality of operating ranges of the electronics device which are obtained by division of an operating area of the electronics device, the operating area being a possible range for the power consumption and the intake air temperature of the electronics device, establishes a plurality of prediction models which are respectively for the plurality of operating ranges and each predicts a future temperature of the heat generator under conditions of the power consumption and the intake air temperature of a corresponding one of the plurality of operating ranges, selects, from among the plurality of prediction models, a prediction model which is established under the conditions of the power consumption and the intake air temperature closest to a current operating condition of the electronics device by calculating a vector distance between a first vector having elements of current power consumption and a current intake air temperature detected by the detector and a second vector having elements of the power consumption and the intake air temperature being the conditions of each prediction model, and selecting the prediction model of the shortest vector distance predicts the future temperature of the heat generator using the corresponding prediction model and determines the manipulated variable of the cooling device based on the predicted temperature.