In a fuel cut period, an adsorbed CO quantity calculation section calculates the amount CATco of CO adsorbed on a catalyst, and an exhaust O2 quantity calculation section calculates the amount GASo2 of O2 in exhaust gases. CO oxidation reaction heat ΔHr produced when the calculated amount CATco of adsorbed CO reacts with the calculated amount GASo2 of O2 in the exhaust gases is calculated by a ΔHr calculation section, and used in estimation of the temperature of the catalyst.