1. A temperature management system to perform temperature management on an electronics device, the system comprising: a detection unit 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 control unit 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 control unit including, a plurality of controllers assigned respectively to a plurality of operating ranges of the electronics device, each of the plurality of controllers configured to control the manipulated variable of the cooling device for a corresponding one of the plurality of operating ranges, the plurality of operating ranges being 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, a plurality of prediction models established respectively for the plurality of operating ranges, the plurality of prediction models included respectively in the plurality of controllers, each of the plurality of prediction models configured to predict 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, and a controller switching unit configured to select a controller of the plurality of controller, the controller using a prediction model of the prediction models, the prediction model being established under the conditions of the power consumption and the intake air temperature closest to a current operating condition of the electronics device, wherein the controller switching unit calculates a vector distance between a first vector and a second vector, the first vector having elements of current power consumption and a current intake air temperature detected by the detection unit, the second vector having elements of the power consumption and the intake air temperature being the conditions of each prediction model, and selects the controller that corresponds to the prediction model of the shortest vector distance, and the selected controller predicts the future temperature of the heat generator using the corresponding prediction model and thereby determines the manipulated variable of the cooling device based on the temperature thus predicted.