  In numerically simulated vibrated beds of powder, we measure temperature
under convection by the generalized Einstein's relation. The spatial
temperature distribution turns out to be quite uniform except for the boundary
layers. In addition to this, temperature remains uniform even if segregation
occurs. This suggests the possibility that there exists some "thermal
equilibrium state" even in a vibrated bed of powder. This finding may lead to a
unified view of the dynamic steady state of granular matter.
