I guess I am naive. I still don't get the problem.
Say we have a block of original kinetic energy K1 that encounters a frictional
surface. It travels a distance d experiencing an average force F over that
distance. I expect that the block will have a new kinetic energy of K2 = K1
-Fd. That is, delta K = W.
Now during that time I expect an amount of thermal energy Q to be generated,
where Q = Fd = W. Now the thermal energy is not simply distributed, but is
shared by the block and the frictional surface and may be conducted or radiated
away in some complicated way.