  We study massless $g^2\Phi^4$-theory at high temperature and with zero
chemical potential. Using modern effective field theory methods,% recently
developed by Braaten and Nieto, we derive the screening mass squared to order
$g^5$. It is demonstrated that the result is renormalization group invariant to
this order in the coupling constant. Renormalization group methods are used to
sum up leading logarithms of $g$.
