Layek　and　Pati　(Phys.　Lett.　A,　2017)　studied　a　nonlinear　system　of　five　coupled　equations,　which　describe　thermal　relaxation　in　Rayleigh-Benard　convection　of　a　Boussinesq　fluid　layer,　heated　from　below.　Here　we　return　to　that　paper　and　use　techniques　from　dynamical　systems　theory　to　analyse　the　codimension-one　Hopf　bifurcation　and　codimension-two　double-zero　BogdanovTakens　bifurcation.　We　determine　the　stability　of　the　bifurcating　limit　cycle,　and　produce　an　unfolding　of　the　normal　form　for　codimension-two　bifurcation　for　the　Layek　and　Pati＇s　model.