We　conduct　a　mathematical　investigation　into　the　dynamical　stability　and　instability　of　the　Rayleigh–Bénard　(abbr.　RB)　problem　for　incompressible　non-Newtonian　fluids　exhibiting　power　law type　behavior,　with　(Formula　presented.).　We　establish　a　critical　threshold,　denoted　as　(Formula　presented.),　and　endeavor　to　demonstrate　that　the　RB　problem　exhibits　exponential　stability　through　the　energy　method　when　the　Rayleigh　number　R　(which　is　influenced　by　the　non-Newtonian　component)　falls　within　the　interval　(Formula　presented.).　Additionally,　we　formulate　an　instability　criterion,　(Formula　presented.),　under　which　the　RB　problem　is　deemed　unstable,　we　aim　to　prove　this　instability　by　employing　a　modified　variational　method.　Our　results　show　that　non-Newtonian　part　has　the　stabilizing　effect　for　thermal　instability.　©　2024　Informa　UK　Limited,　trading　as　Taylor　&　Francis　Group.