The analysis of Balmer-dominated optical spectra from nonradiative (adiabatic) SNRs has shown that the ratio of the electron to proton temperature at the blast wave is close to unity at v(s) approximate or smaller than 400 km s(-1) but declines sharply down to the minimum value of m(e) /m(p) dictated by the jump conditions at shock speeds exceeding 2000 km s(-1). We propose a physical model for the heating of electrons and ions in non-cosmic-ray-dominated, strong shocks (v(s) 400 km s(-1)) wherein the electrons are heated by lower hybrid waves immediately ahead of the shock front. These waves arise naturally from the cosmic ray pressure gradient upstream from the shock. Our model predicts a nearly constant level of electron heating over a wide range of shock speeds, producing a relationship (T(e)/T(p))sub 0 proportional to v(-2/s) (proportional to M(-2)) that is fully consistent with the observations.

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