Collisionless shock waves in supernova remnants and the solar wind heat electrons less effectively than they heat ions, as is predicted by kinetic simulations. However, the values of T ( e )/T ( p ) inferred from the H alpha profiles of supernova remnant shocks behave differently as a function of Mach number or Alfven Mach number than what is measured in the solar wind or predicted by simulations. Here we determine T ( e )/T ( p ) for supernova remnant shocks using H alpha profiles, shock speeds from proper motions, and electron temperatures from X-ray spectra. We also improve the estimates of sound speed and Alfven speed used to determine Mach numbers. We find that the H alpha determinations are robust and that the discrepancies among supernova remnant shocks, solar wind shocks, and computer-simulated shocks remain. We discuss some possible contributing factors, including shock precursors, turbulence, and varying preshock conditions.