In order to follow a diet, two things are necessary. No exorphins and no acellular carbohydrates. Once that occurs, calories or rather bio-available energy, calories minus non exercise thermogenenis, becomes the accounting for weight change. Now fat burning produces more non exercise thermogenenis than carbohydrate burning. The body then adjusts for the energy. something like this http://www.biologymad.com/resources/A2%20Homeostasis.pdf.
But there is slop between wasting heat and conserving heat, but besides me cares. Hystorisis.