Non-radiative shocks in partially neutral gas produce faint optical spectra which are dominated by the Balmer lines of hydrogen, with each line profile exhibiting broad and narrow components. The velocity width of the broad Balmer line and the ratio of broad to narrow line fluxes are sensitive to both the shock speed and the degree of electron-proton temperature equilibration at the shock transition. In addition, the relative widths of such UV resonance lines as He II 1640, C IV 1550, N V 1240 and O VI 1036 are sensitive to both the electron-proton and ion-ion temperature equilibration at the shock. With these diagnostics, we can map the dependence of the temperature equilibration with shock speed in supernova remnants. The data indicate an inverse square dependence of T_e / T_p on the shock speed, a result which suggests an equilibration process operating in the cosmic ray precursor, and which constrains the range of equilibration processes allowed in high Mach number, non-relativistic shocks.