  We measure the temperature of a 2D electron gas in GaAs from the thermopower
of a one-dimensional ballistic constriction, using the Mott relation to confirm
the calibration from the electrical conductance. Under hot electron conditions,
this technique shows that the power loss by the electrons follows a $T^5$
dependence in the Gruneisen-Bloch regime, as predicted for acoustic phonon
emission with a screened piezoelectric interaction. An independent measurement
using conventional thermometry based on Shubnikov-de Haas oscillations gives a
$T^3$ loss rate; we discuss reasons for this discrepancy.
