  We study the realization of dimensional reduction and the validity of the
hard thermal loop expansion for lambda phi^4 theory at finite temperature,
using an environmentally friendly finite-temperature renormalization group with
a fiducial temperature as flow parameter. The one-loop renormalization group
allows for a consistent description of the system at low and high temperatures,
and in particular of the phase transition. The main results are that
dimensional reduction applies, apart from a range of temperatures around the
phase transition, at high temperatures (compared to the zero temperature mass)
only for sufficiently small coupling constants, while the HTL expansion is
valid below (and rather far from) the phase transition, and, again, at high
temperatures only in the case of sufficiently small coupling constants. We
emphasize that close to the critical temperature, physics is completely
dominated by thermal fluctuations that are not resummed in the hard thermal
loop approach and where universal quantities are independent of the parameters
of the fundamental four-dimensional theory.
