This　paper　concerns　the　non-isentropic　Euler-Maxwell　equations　for　plasmas　with　short　momentum　relaxation　time.　With　the　help　of　the　Maxwell-type　iteration,　it　is　obtained　that,　as　the　relaxation　time　tends　to　zero,　periodic　initial-value　problem　of　certain　scaled　non-isentropic　Euler-Maxwell　equations　has　unique　smooth　solutions　existing　in　the　time　interval　where　the　corresponding　classical　drift-diffusion　model　has　smooth　solutions.　Meanwhile,　we　justify　a　formal　derivation　of　the　corresponding　drift-diffusion　model　from　the　non-isentropic　Euler-Maxwell　equations.　(C)　2011　Elsevier　Inc.　All　rights　reserved.