So currently, Max Capes and Cooking Skill Cape mean you don't burn food. However this only works with the standard Max cape (at least from what I've tested with the ones I own).
I've tried it with a Fire Max Cape, Infernal Max cape, Assembler Max Cape and Imbued Guthix Max Cape.
I think it would be a nice addition to include these max capes to also have the same effect as the Max Cape/Cooking Skill Cape.