Or is heat merely a catalyst to get the job done?
In a closed system, if I use heat to raise the temperature of 10 kg of water from room temperature to 80 degrees celsius, that heat could be recaptured as the water cools. If I use an equivalent amount of heat to raise the temperature of a 10kg turkey, can I recapture the same amount of heat as the turkey cools.
A good chunk of the heat goes to making protein changes in the turkey meat. That’s what heating meat does, makes those changes that turn raw muscle into edible meat. That energy can’t be recovered.
IANA Physics major.
What you’re asking, I think, is whether the chemical reactions in ‘cooking food’ (or specifically ‘roasting a turkey’) are net-endothermic or not. If yes, then not all the energy that goes into the cooking process is simply to raise the temperature of the food, some of it will be converted into the chemical changes of the cooking process. (Probably not the technically correct way to phrase that, hopefully you get the idea.)
The question is complicated, because even in the turkey-roasting question, there are a lot of different chemical reactions going on. But the most obvious one is protein denaturation, (which is what makes cooked turkey easier to chew than raw turkey,) and based on a brief google search, it looks like that’s endothermic at typically high (higher than room temperature?) conditions.
I’ll also point out that there are myriad heat losses in the process; conduction from the oven out into the wall, the floor, the kitchen counter if that’s close enough to your range, and convection of air and steam, especially when you open the over door to baste. 
On edit: Thanks for the link, Telemark, but does that article specifically say that heat is absorbed by the changes, instead of being a catalyst for the chemical reactions? I didn’t see anything specifically talking about endothermic or exothermic reactions there.