In a medium with spatial dispersion the power Pabs dissipated per unit volume by an electro-magnetic wave differs from (J.E) by the divergence of a vector which is interpreted as the correction delta Skin to the Poynting flux due to the coherent particle motion in the field. The authors obtain expressions for Pabs and delta Skin in hot, inhomogeneous, weakly collisional plasmas by evaluating the time-averaged rate of change of the total kinetic energy density of charged particles, generalizing a method suggested by McVey et al. (Phys. Rev. Lett. vol.55, p.507, 1985). The authors prove that these expressions are consistent with the time averaged Poynting theorem for Maxwell equations. By specializing them to uniform and plane-stratified geometries, they derive some interesting properties of wave-plasma energy exchanges, and they check that the well known expressions for Pabs and delta Skin in the case of a plane wave propagating in an infinite homogeneous plasma are recovered in the appropriate limit.