There are two big things going on when you cook meat:
- bringing it up to the desired temperature
- holding it there long enough for desired changes to occur
For some meat, the temperature is basically all that matters. The most common example of this is a steak: once it's the temperature you want, it's done. You might finish it off by searing it to cook the outside a bit extra, but the doneness of the bulk of the meat depends purely on the temperature.
For other kind of meat, the temperature is just the first step, and the cooking you really want happens as you hold it there. Anything with a really long cooking time is likely in this category, like the 24-48 hour pork cheek you mentioned, or perhaps more commonly, slow-cooked pork shoulder or ribs. That long cooking lets the connective tissue break down (notably collagen turning to gelatin), taking it from chewy and tough to pull-apart tender. It'll break down at temperatures as low as 50C/120F, but as you increase the temperature it'll break down faster and faster, up to 80C/180F.
Some of those reactions might be endothermic, but protein hydrolysis is actually slightly exothermic. The energy is also way, way smaller than the energy you use to heat the meat - for cooking purposes, you can ignore it. In any case, trying to model heat transfer and heat input is kind of pointless: it's the reaction rate that matters, not the energy you're using/wasting to keep it at that temperature. The reaction rate does increase with temperature, as mentioned above, but again that's about temperature, not energy input.
So how does that all connect to your energy hypothesis?
Bringing meat up to the desired temperature is basically all about energy: you have to transfer a fixed amount of heat energy to bring a given amount of meat to a given temperature. So in that sense, you're spot-on.
But when you're holding meat at a temperature to cook it, you're not transferring significant heat into it anymore. It's really just about time. The amount of time it takes does often depend on the temperature, since the reaction rates are temperature-dependent, and that's why you've see the variation in time and temperature in recipes. But it's no longer a simple matter of energy input as you guessed. Yes, you'll have an initial period of bringing the meat up to temperature, which is simple heat transfer, but the real cooking happens after that.