Great question! Jet engines are already extremely heat efficient. Micro-managing the small heat losses left would likely introduce weight or cost penalties that would negate any potential gains. Compressor losses and aerodynamic losses would probably yield better results.
Heat transfer losses in jet engines can be reduced with thermal barrier coatings (TBCs), advanced cooling (film/transpiration), high-temperature alloys, and optimised aerodynamic designs. Increasing the pressure ratio (OPR) further improves thermal efficiency.
Wisdom Simwila Kalunga The parameters that you list are the basic building blocks of all gas turbines. All manufacturers try to improve compressors, blade cooling etc. These are not heat transfer losses, as you originally asked: what are you looking for?