A combustor for burning the untreated exhaust of an internal combustion engine heats and burns the exhaust prior to release into the atmosphere, or prior to introduction into a downstream treatment system such as a catalytic converter. The combustor defines a novel, passive flame holder in combination with an igniter, whereby the exhaust continues to burn, without assist, once ignited. Managed air injection may be employed. The combustor is configured to fit within standard exhaust systems with a minimum of modification to the overall exhaust assembly. The combustor is particularly useful in cold start conditions for increasing the temperature of the exhaust to catalytic converter operating temperatures and for use in small engine applications where exhaust has heretofore been released untreated.