  We calculate numerically the quasiparticle effective mass (m*)
renormalization as a function of temperature and electron density in two- and
three-dimensional electron systems with long-range Coulomb interaction. In two
dimensions, the leading temperature correction is linear and positive with the
slope being a universal density independent number in the high density limit.
We predict an enhancement of the effective mass at low temperatures and a
non-monotonic temperature dependence at higher temperatures (T/T_F ~ 0.1) with
the peak shifting toward higher temperatures as density decreases. In three
dimensions, we find that the effective mass temperature dependence is nonlinear
and non-universal, and depends on the electron density in a complicated way. At
very high densities, the leading correction is positive, while at lower
densities it changes sign and the effective mass decreases monotonically from
its zero temperature value with increasing temperature.
