An automatic transmission calculates a current thermal load state of the frictional element, predicts (S24, S31), prior to the start of the shift, a heat generation amount of the frictional element if the shift is performed in the first shift mode, predicts (S25, S32) 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, and either performs (S28, S38) the shift in a second shift mode, in which a heat generation amount is lower than that of the first shift mode, or prohibits (S39) the shift when the predicted thermal load state upon shift completion is inside a predetermined region.