  Supersymmetric renormalization group (RG) flow equations for the effective
superpotential of the three-dimensional Wess-Zumino model are derived at zero
and non-zero temperature. This model with fermions and bosons interacting via a
Yukawa term possesses a supersymmetric analogue of the Wilson-Fisher
fixed-point. At zero temperature we determine the phase-transition line in
coupling-constant space separating the supersymmetric from the
non-supersymmetric phase. At finite temperature we encounter dimensional
reduction from 3 to 2 dimensions in the infrared regime. We determine the
finite-temperature phase diagram for the restoration of the global
$Z_2$-symmetry and show that for temperatures above the $Z_2$ phase transition
the pressure obeys the Stefan-Boltzmann law of a gas of massless bosons in 2+1
dimensions.
