The point I'm making is a dry hay box will not generate its own heat. Put something cold in it and It wont be cooked 5/6hrs later. Try it if you doubt me.
But a wet hay box will.!! Exactly the same as a compost heat. 2" of wet compressed organic matter gets hot! Again try it if you doubt me. A good compost heap steams when you turn it over. All gardeners know this!!
No-one is disagreeing with you about the heat generated by damp grass/hay - the point was that the 'hay box' described earlier does not rely on 'generated' heat but just insulating the heat to continue cooking food that has been brought up to temperature by boiling or otherwise.