A temperature estimation device for friction engaging elements including an execution device and a storage device is provided. The storage device stores mapping data that defines mapping. The mapping includes, as an input variable, a heat amount variable that is a variable indicating an amount of heat generated by the friction engaging elements during the shifting of the transmission and a shifting variable indicating the friction engaging elements to be engaged at the time of the shifting of the transmission, and, as an output variable, the temperature. The execution device executes an acquisition process of acquiring a value of the input variable and a calculation process of inputting the value of the input variable acquired by the acquisition process into the mapping to calculate a value of the output variable.