  We apply the $\delta$-expansion perturbation scheme to the $\lambda \phi^{4}$
self-interacting scalar field theory in 3+1 D at finite temperature. In the
$\delta$-expansion the interaction term is written as $\lambda (\phi^{2})^{ 1 +
\delta}$ and $\delta$ is considered as the perturbation parameter. We compute
within this perturbative approach the renormalized mass at finite temperature
at a finite order in $\delta$. The results are compared with the usual
loop-expansion at finite temperature.
