1A) the act of preparing food for eating, especially by heating
1B) a manner of preparing food
To say that "cooking" requires heat is inaccurate. It's the usual qualification, but is not necessary in a general sense.
and more to the point: If some one is proud of their sandwich, why would you take that from them? dick move. Even Gordon Fucking Ramsey had to start somewhere.
Cooking, also known as cookery or professionally as the culinary arts, is the art, science and craft of using heat to make food more palatable, digestible, nutritious, or safe.
Wikipedia says so. Can someone make a really good sandwich without cooking? Sure. I wouldn't even pull an "um ackshuly" on them. But you're putting words in OP's mouth now.
Also, I wonder whose more definitive on the meaning of words? The long-standing, generally recognized as the definitive dictionary for US-English... or... wikipedia?