  We discuss the universal critical behavior of a selfinteracting scalar field
theory at finite temperature as obtained from approximate solutions to
nonperturbative renormalization group (RG) equations. We employ a formulation
of the RG-equations in real-time formalism which is particularly well suited
for a discussion of the thermal behavior of theories which are weakly coupled
at T=0. We obtain the equation of state and critical exponents of the theory
with a few percent accuracy even for a relatively simple approximation to the
exact renormalization group equations.
