A method of regenerating a particulate filter that traps combustible particulates in an exhaust system of an internal combustion engine that has a variable valve actuation mechanism for varying the opening and closing times of exhaust valves that control flow from cylinders of the engine into the exhaust system and for varying the opening and closing times of intake valves that control flow into the cylinders from an intake system of the engine, the method comprising: with the engine running under its own power, operating the variable valve actuation mechanism to decrease the fraction of an engine operating cycle for which both intake and exhaust valves (18, 24) for a respective cylinder are simultaneously open as a piston in the respective cylinder approaches top dead center to complete an exhaust stroke, and as a result, elevate the temperature of flow through the exhaust system to a temperature that is effective to combust particles that have been trapped by the filter, thereby regenerating the filter, including the steps of measuring the temperature of flow through the exhaust system, of comparing the measured temperature with a reference that defines a low temperature limit that distinguishes between a condition calling for further elevation of the temperature of flow through the exhaust system and a condition that does not call for such further elevation, of altering injection of fuel into the respective cylinder to cause the temperature of flow out of the respective cylinder into the exhaust system to increase if the comparison discloses that the measured temperature does not exceed the reference, of measuring the temperature of flow through the exhaust system while the altered injection of fuel into the respective cylinder is causing the temperature of flow out of the respective cylinder into the exhaust system to increase, of comparing the latter measured temperature with a reference that defines a high temperature limit for the flow, and of discontinuing the altered injection of fuel into the respective cylinder if the latter measured temperature exceeds the latter reference, including the further steps of measuring the temperature of flow through the exhaust system after the altered injection of fuel into the respective cylinder has been discontinued, of comparing the latter measured temperature with the reference that defines a high temperature limit for the flow, and if the latter measured temperature exceeds the latter reference, of operating the variable valve actuation mechanism to increase the fraction of an engine operating cycle for which both intake and exhaust valves (18, 24) for a respective cylinder are simultaneously open as a piston in the respective cylinder approaches top dead center to complete an exhaust stroke so as to reduce the temperature of flow below the high temperature limit. with the engine running under its own power, operating the variable valve actuation mechanism to decrease the fraction of an engine operating cycle for which both intake and exhaust valves (18, 24) for a respective cylinder are simultaneously open as a piston in the respective cylinder approaches top dead center to complete an exhaust stroke, and as a result, elevate the temperature of flow through the exhaust system to a temperature that is effective to combust particles that have been trapped by the filter, thereby regenerating the filter, including the steps of measuring the temperature of flow through the exhaust system, of comparing the measured temperature with a reference that defines a low temperature limit that distinguishes between a condition calling for further elevation of the temperature of flow through the exhaust system and a condition that does not call for such further elevation, of altering injection of fuel into the respective cylinder to cause the temperature of flow out of the respective cylinder into the exhaust system to increase if the comparison discloses that the measured temperature does not exceed the reference, of measuring the temperature of flow through the exhaust system while the altered injection of fuel into the respective cylinder is causing the temperature of flow out of the respective cylinder into the exhaust system to increase, of comparing the latter measured temperature with a reference that defines a high temperature limit for the flow, and of discontinuing the altered injection of fuel into the respective cylinder if the latter measured temperature exceeds the latter reference, including the further steps of measuring the temperature of flow through the exhaust system after the altered injection of fuel into the respective cylinder has been discontinued, of comparing the latter measured temperature with the reference that defines a high temperature limit for the flow, and if the latter measured temperature exceeds the latter reference, of operating the variable valve actuation mechanism to increase the fraction of an engine operating cycle for which both intake and exhaust valves (18, 24) for a respective cylinder are simultaneously open as a piston in the respective cylinder approaches top dead center to complete an exhaust stroke so as to reduce the temperature of flow below the high temperature limit.