This　article　concerns　the　initial-boundary　layer　effects　of　the　3D　incompressible　Boussinesq　system　for　Rayleigh-Bénard　convection　with　ill-prepared　initial　data.　We　consider　a　non-slip　boundary　condition　for　the　velocity　field　and　inhomogeneous　Dirichlet　boundary　condition　for　the　temperature.　By　means　of　multi-scale　analysis　and　matched　asymptotic　expansion　methods,　we　establish　an　accurate　approximating　solution　for　the　viscous　and　diffusive　Boussinesq　system.　We　also　study　the　convergence　of　the　infinite　Prandtl　number　limit.　©　2020　Texas　State　University.