  Seventy measurements of electron heating at the Earth's quasi-perpendicular
bow shock are analyzed in terms of Maxwellian-temperatures obtained from fits
to the core electrons that separate thermal heating from supra-thermal
acceleration. The perpendicular temperatures are both greater and lesser than
expected for adiabatic compression. The average parallel and perpendicular
heating is the same. These results are explained because, over the electron
gyroradius, $\delta B/B\sim 1$ and $e\delta \phi/T_e\sim 1$, so electron
trajectories are more random and chaotic than adiabatic. Because density
fluctuations are also large, trapping and wave growth in density holes may be
important.
