An internal-combustion-engine warm-up apparatus includes: a post-processing apparatus; a heater arranged upstream of the post-processing apparatus on the exhaust path; a circulation path where air having passed through the post-processing apparatus is fed back to an upstream side of the heater; an air pump that is a blower that feeds air heated by the heater to the post-processing apparatus; a coolant flow path; a heat exchanger; and a control apparatus that controls operation of the heater and the blower, and in a state where the engine is stopped, the control apparatus causes the heater and the air pump to operate, and causes the air heated by the heater to be supplied to the post-processing apparatus and the heat exchanger.