An exothermic heat generating apparatus is preferably used as a heat source for rapidly heating in a vehicle or the like, to enable repetition of stable exothermic reaction for long terms.In the apparatus, a closed cycle includes a reactor filled with alkali earth oxide, a water tank, a water supply pipe to supply water from the water tank into the reactor, and a reflux pipe to return the water from the reactor to the water tank. Reversible reaction between the alkali earth oxide and the water is carried out in the closed system. A pump supplies the reactor with water, and a solenoid valve controls a water supply. The exothermic heat generating apparatus uses heat generated by hydration reaction of the alkali earth oxide to rapidly heat a catalytic section, a cooling water section, an air intake section and the like at a time of engine start-up.