  We demonstrate local detection of the electron temperature in a
two-dimensionalmicrodomain using a quantum dot. Our method relies on the
observation that a temperature bias across the dot changes the functional form
of Coulomb-blockade peaks. We apply our results to the investigation of
electron-energy relaxation at subkelvin temperatures, find that the energy flux
from electrons into phonons is proportional to the fifth power of temperature,
and give a measurement of the coupling constant.
