  Heating of charged particles via collisionless shocks, while ubiquitous in
the universe, is an intriguing yet puzzling plasma phenomenon. One outstanding
question is how electrons and ions approach an equilibrium after they were
heated to different immediate-postshock temperatures. In order to fill the
significant lack of observational information of the downstream
temperature-relaxation process, we observe a thermal-dominant X-ray filament in
the northwest of SN~1006 with Chandra. We divide this region into four layers
with a thickness of 15$^{\prime\prime}$ or 0.16 pc each, and fit each spectrum
by a non-equilibrium ionization collisional plasma model. The electron
temperature was found to increase toward downstream from 0.52-0.62 keV to
0.82-0.95 keV on a length scale of 60 arcsec (or 0.64 pc). This electron
temperature is lower than thermal relaxation processes via Coulomb scattering,
requiring some other effects such as plasma mixture due to turbulence and/or
projection effects, etc, which we hope will be resolved with future X-ray
calorimeter missions such as XRISM and Athena.
