Does the definition of "cooking" imply heat?
Neither "yes" nor "no" is a suitable answer to that question. 

First, there is no "the definition" of cooking. I am sure you can turn up several formal definitions, and my best guess is that some will require heat and others won't. 

Second, and probably more important, humans don't think in definitions. You are asking if a given action belongs to the category "cooking methods". A definition works by ticking off features some element has to have to belong to a category. Real human categories (in everyday thinking, as opposed to formally defined ones in the sciences) depend on the closeness of an element to a prototype element. This closeness is gradual, and there is no demarcation to say where the category ends. 

Keeping this in mind, all prototypical forms of cooking clearly involve heat, so the ones which don't involve it have a weaker membership in the "cooking methods" category than those which do. But it is impossible to pronounce whether they fall inside or outside of the category. Different people will answer that question differently, and I suspect that even the same person may give different answers in different contexts. 

To make it even more complicated, "apply heat" is not the single thing which makes a food-related action resemble stewing (or whatever you take the prototype cooking method to be). So different things you do to food without heat will have a different grade of belonging to the "cooking" category. 

People tend to not be aware of all that, and usually trust their intuition to take one side or the other. So you'll find people on both sides who insist they are right, and can rationalize it with some kind of plausibly sounding argument. Reality is more complicated than that, and if you try to prove one of the sides wrong, you will end up in a flame war going nowhere.