We　are　concerned　with　the　stability　and　convergence　rate　of　planar　stationary　solution　to　the　compressible　heat　conducting　gas　in　half　space　ℝ3+　under　outflow　condition.　(1)　It　is　shown　that　a　corresponding　planar　stationary　solution　is　time　asymptotically　stable　in　three　cases　(i.e.,　supersonic,　subsonic,　and　transonic),　respectively,　provided　the　initial　perturbation　in　a　certain　Sobolev　space　and　the　boundary　strength　are　sufficiently　small.　(2)　Moreover,　the　convergence　rate　of　the　solution　toward　the　stationary　solution　is　obtained,　provided　that　the　initial　perturbation　belongs　to　the　weighted　Sobolev　space.　Precisely,　we　obtain　an　algebraic　decay　rate　provided　that　an　initial　perturbation　decays　in　a　tangential　direction　with　the　algebraic　rate　for　a　supersonic　flow.　The　corresponding　algebraic　convergence　rate　is　also　obtained　for　a　transonic　flow,　which　is　worse　than　that　for　the　supersonic　flow　due　to　a　degenerate　property　of　the　transonic　flow.　Each　proof　is　given　by　deriving　a　priori　estimates　of　the　perturbation　from　the　stationary　wave　by　using　a　time　and　space　weighted　energy　method.　©　by　SIAM.　Unauthorized　reproduction　of　this　article　is　prohibited.