An engine cooling system comprising an exhaust enclosure formed in an engine compartment of a work machine. An exhaust processing system is situated within the exhaust enclosure. The exhaust enclosure is bounded in part by spaced upper and lower panels that are exposed to the ambient environment. At least one opening is formed in each panel. When an engine and fan also contained within the engine compartment are shut down, ambient air flows into the exhaust enclosure through the opening in the lower panel. The air flows around the exhaust processing system and back into the ambient environment through the opening formed in the upper panel.