  The linear $\delta$ expansion is used to obtain corrections up to
O$(\delta^2)$ to the self-energy for a complex scalar field theory with a
$\lambda (\phi^{\star}\phi)^2$ interaction at high temperature and non-zero
charge density. The calculation is done in the imaginary-time formalism via the
Hamiltonian form of the path integral. Nonperturbative results are generated by
a systematic order by order variational procedure and the dependence of the
critical temperature on the chemical potential $\mu$ is obtained.
