A control apparatus for an internal combustion engine executes a detection process upon satisfaction of all detection preconditions including a stopped condition that a temperature-increasing process has been stopped; determines Whether all the detection preconditions except the stopped condition are satisfied, during the temperature-increasing process; executes a gradually-changing-and-stopping process of stopping the temperature-increasing process by gradually changing the air-fuel ratios in the cylinders to a target air-fuel ratio set based on an operation state of the internal combustion engine after stop of the temperature-increasing process, when a negative determination is made and a temperature-increasing process stop request has been issued; and executes a promptly-stopping process of stopping the temperature-increasing process by changing the air-fuel ratios in the cylinders to the target air-fuel ratio within a shorter time period than that of the gradually-changing-and-stopping process, when an affirmative determination is made and a temperature-increasing process stop request has been issued.