The　one-dimensional　motion　of　compressible　viscous　and　heat-conductive　fluid　is　investigated　in　the　half　space.　By　examining　the　sign　of　fluid　velocity　prescribed　on　the　boundary,　initial　boundary　value　problems　with　Dirichlet　type　boundary　conditions　are　classified　into　three　cases:　impermeable　wall　problem,　inflow　problem　and　outflow　problem.　In　this　paper,　the　asymptotic　stability　of　the　rarefaction　wave,　boundary　layer　solution,　and　their　combination　is　established　for　both　the　impermeable　wall　problem　and　the　inflow　problem　under　some　smallness　conditions.　The　proof　is　given　by　an　elementary　energy　method.