This　paper　completes　a　numerical　research　on　steady　momentum　and　heat　transfer　in　power-law　fluids　in　a　channel.　Weakly　compressible　laminar　fluids　are　studied　with　no　slip　at　the　walls　and　uniform　wall　temperatures.　The　full　governing　equations　are　solved　by　continuous　finite　element　method.　Three　thermal　conductivity　models　are　adopted　in　this　paper,　that　is,　constant　thermal　conductivity　model,　thermal　conductivity　varying　as　a　function　of　temperature　gradient,　and　a　modified　temperature-gradient-dependent　thermal　conductivity　model.　The　results　are　compared　with　each　other　and　the　physical　characteristics　for　values　of　parameters　are　also　discussed　in　details.　It　is　shown　that　the　velocity　curve　from　the　solution　becomes　straight　at　higher　power-law　index.　The　effects　of　Reynolds　numbers　on　the　dilatant　fluid　and　the　pseudo-plastic　look　similar　to　each　other　and　their　trends　can　be　easily　predicted.　Furthermore,　for　different　models,　the　temperature　curves　also　present　pseudo-plastic　and　dilatant　properties.