Is some of the energy of food lost during digestion?
Typically, catabolic reactions such as the hydrolysis of food stuffs into their monomers is an exothermic process. This includes conversion of proteins into amino aids, starchs into monosaccharides and fats into fatty acids plus glycerol. As an example, hydrolysis of a peptide bond linking the amino acids in a protein liberates 8-16 kJ/mol of energy. 
https://en.wikipedia.org/wiki/Peptide_bond

So, that means a certain amount of the energy in food is liberated in the gut. But this is very minimal compared to the amount yet to be liberated, and harvested, as the many other bonds in the monomers are further broken down during cellular respiration.

A bit of research from a few different sites suggests the gut temperature is not meaningfully higher that the core body temperature measured in, say, the anus or vagina. https://en.wikipedia.org/wiki/Human_body_temperature  Any heat liberated from digestion in the gut must be slow enough to be absorbed into the bulk of the body without accumulating in the gut.