The factory foam is missing from one side of the doghouse and the foam on the other side is not in great shape. Has anyone tried using Great Stuff Foam to replace it?
Usually products have an 800 number on the can. Call the number if one is listed and talk to the company about your idea....they can advise you of its safety, etc.. They may even have a product for high temperature applications.
There are many companies that make sound proofing for engine compartments and hot exhaust system. Some are produced for race cars.