This　work　is　concerned　with　the　periodic　problem　for　compressible　non-isentropic　Euler-Maxwell　systems　with　a　temperature　damping　term　arising　in　plasmas.　For　this　problem,　we　prove　the　global　in　time　existence　of　a　smooth　solution　around　a　given　non-constant　steady　state　with　the　help　of　an　induction　argument　on　the　order　of　the　mixed　time-space　derivatives　of　solutions　in　energy　estimates.　Moreover,　we　also　show　the　convergence　of　the　solution　to　this　steady　state　as　the　time　goes　to　the　infinity.　This　phenomenon　on　the　charge　transport　shows　the　essential　relation　of　the　systems　with　the　non-isentropic　Euler-Maxwell　and　the　isentropic　Euler-Maxwell　systems.　Copyright　(c)　2015　John　Wiley　&　Sons,　Ltd.