An exhaust system for use with a combustion engine is disclosed. The exhaust system may have an exhaust passage, a particulate filter located within the exhaust passage, and a heating device located to selectively heat matter collected within the particulate filter. The exhaust system may also have a controller configured to determine an amount of matter collected within the particulate filter exceeding a threshold amount, and to activate the heating device in a first operating mode to regenerate the particulate filter based on the amount of collected matter. The controller may be further configured to detect a temperature constraining condition of the combustion engine, to determine an amount of oxygen within the flow of exhaust during the temperature constraining condition, and to activate the heating device in a second operating mode to constrain a regeneration temperature of the particulate filter based on the amount of oxygen within the flow of exhaust.