  The non-commutative version of the euclidean $g^2\phi^4$ theory is
considered. By using Wilsonian flow equations the ultraviolet renormalizability
can be proved to all orders in perturbation theory. On the other hand, the
infrared sector cannot be treated perturbatively and requires a resummation of
the leading divergencies in the two-point function. This is analogous to what
is done in the Hard Thermal Loops resummation of finite temperature field
theory. Next-to-leading order corrections to the self-energy are computed,
resulting in $O(g^3)$ contributions in the massless case, and $O(g^6\log g^2)$
in the massive one.
