A exhaust catalyst temperature estimating apparatus for estimating an exhaust catalyst temperature of an exhaust catalyst in which a catalyst is loaded on a support and arranged in an exhaust system of an internal combustion engine, the exhaust catalyst temperature estimating apparatus being characterized in that: the exhaust catalyst temperature estimating apparatus estimates the exhaust catalyst temperature using a first model formula to calculate a current exhaust catalyst temperature of the exhaust catalyst based on a parameter corresponding to a current exhaust gas status; and the first model formula is empirically determined such that an exhaust catalyst temperature that excludes heat generated by a chemical reaction is calculated for the parameter by using the support prior to being loaded with the catalyst, or is a physical formula of the support prior to being loaded with the catalyst such that an exhaust catalyst temperature excludes heat generated by a chemical reaction is calculated for the parameter; the exhaust catalyst temperature estimating apparatus uses a second model formula to calculate the current exhaust catalyst temperature of the exhaust catalyst based on the parameter corresponding to the current exhaust gas status; the second model formula is empirically determined such that an exhaust catalyst temperature in the presence of heat generated by a chemical reaction is calculated for the parameter by using the exhaust catalyst supporting the catalyst, or is a physical formula of the exhaust catalyst supporting the catalyst such that an exhaust catalyst temperature in the presence of heat generated by a chemical reaction is calculated for the parameter; and the exhaust catalyst temperature estimating apparatus estimates the current exhaust catalyst temperature using the first model formula when a prescribed condition is satisfied, and estimates the current exhaust catalyst temperature using the second model formula when the prescribed condition is not satisfied. the exhaust catalyst temperature estimating apparatus estimates the exhaust catalyst temperature using a first model formula to calculate a current exhaust catalyst temperature of the exhaust catalyst based on a parameter corresponding to a current exhaust gas status; and the first model formula is empirically determined such that an exhaust catalyst temperature that excludes heat generated by a chemical reaction is calculated for the parameter by using the support prior to being loaded with the catalyst, or is a physical formula of the support prior to being loaded with the catalyst such that an exhaust catalyst temperature excludes heat generated by a chemical reaction is calculated for the parameter; the exhaust catalyst temperature estimating apparatus uses a second model formula to calculate the current exhaust catalyst temperature of the exhaust catalyst based on the parameter corresponding to the current exhaust gas status; the second model formula is empirically determined such that an exhaust catalyst temperature in the presence of heat generated by a chemical reaction is calculated for the parameter by using the exhaust catalyst supporting the catalyst, or is a physical formula of the exhaust catalyst supporting the catalyst such that an exhaust catalyst temperature in the presence of heat generated by a chemical reaction is calculated for the parameter; and the exhaust catalyst temperature estimating apparatus estimates the current exhaust catalyst temperature using the first model formula when a prescribed condition is satisfied, and estimates the current exhaust catalyst temperature using the second model formula when the prescribed condition is not satisfied.