  We use the non-perturbative renormalization group to clarify some features of
perturbation theory in thermal field theory. For the specific case of the
scalar field theory with O(N) symmetry, we solve the flow equations within the
local potential approximation. This approximation reproduces the perturbative
results for the screening mass and the pressure up to order g^3, and starts to
differ at order g^4. The method allows a smooth extrapolation to the regime
where the coupling is not small, very similar to that obtained from a simple
self-consistent approximation.
