A method for controlling an engine includes receiving a request to regenerate a particulate matter filter and regulating, in response to the request, operation of the engine and an electric heater that heats an inlet surface of the filter such that for a first period, the heater maintains the inlet surface within a first temperature range above a regeneration temperature of the filter and combustion of a first mass of accumulated PM within the filter is initiated, for a second period following the first period, exhaust cools the inlet surface to within a second temperature range below the regeneration temperature and combustion of the first mass is inhibited, and for a third period following the second period, the inlet surface is maintained within a third temperature range above the regeneration temperature and a second mass of the accumulated PM is combusted. A related control system is also provided.