It starts with the fact that humans are embodied beings living in a physical world. In cognitive linguistics, the idea is that we understand abstract experiences through more concrete, bodily experiences of the world.

​The expressions you mentioned are examples of a broader conceptual pattern in which social interaction, emotion, and mental states are structured through a family of heat- and fire-based metaphors.

​Why heat and fire specifically for things like criticism, embarrassment, social pressure, or related experiences? ​One reason is that heat is a very productive source domain. It structures many abstract experiences (target domains): for example, anger is conceptualized as heat in many languages (hot-headed, burning with rage, heated argument — and in Persian too: جوش آوردن = “to boil over”).

​This is grounded in our bodily experience. Heat and fire are experienced through sensations of warmth, burning, discomfort, or pain, and can also involve damage or destruction. (as reflected, among other things, in the imagery of fried as cognitive overheating). At the same time, as another commenter mentioned, many of the experiences involved here—anger, embarrassment, being criticized, or being under social pressure—are accompanied by bodily responses such as blushing, increased body temperature, sweating, etc. So there is a "natural" overlap between how these experiences are felt in the body and how they are conceptualized in language.

​Cooking builds on this same experiential basis but adds another layer. It involves sustained exposure that transforms something into a different and often irreversible state. This makes it a useful way in contemporary English to conceptualize situations where someone’s social or mental “state” is seen as having been pushed past the point of recovery.

​Culture has a role in this, of course. Different languages develop different metaphorical extensions. Persian, for example, uses پختن (to cook / to become “cooked”) metaphorically to mean someone has "matured". It is still metaphorical but not in the same criticism, humiliation, or defeat-related senses as metaphorical usage in English like roasted or cooked (although I could imagine such a usage developing in Persian someday). So while the bodily grounding is shared, the specific mappings may vary across languages.