An automatic transmission calculates a current thermal load state of the frictional element, predicts (S41), prior to the start of the shift, a heat generation amount of the frictional element during the shift, predicts (S42) a thermal load state of the frictional element upon shift completion on the basis of the current thermal load state of the frictional element and the predicted heat generation amount, determines (S43, S44, S45) whether to permit or prohibit the shift on the basis of the predicted thermal load state upon shift completion, and halts the determination as to whether to permit or prohibit the shift, made on the basis of the predicted thermal load state upon shift completion, when a shift mode of the shift is a second shift mode in which the heat generation amount is smaller than that of a first shift mode.