Résumé
We illustrate how our recently developed renormalization group optimized perturbation (RGOPT) efficiently resums perturbative expansions in thermal field theories. The residual renormalization scale dependence of optimized thermodynamical quantities is drastically improved as compared to either standard perturbative expansions, or related methods such as the screened perturbation or (resummed) hard-thermal-loop perturbation. Our approach is illustrated briefly for the nonlinear sigma model, as a toy model for thermal QCD. Finally, preliminary applications of RGOPT to hard thermal loop resummation for the QCD pressure are sketched.