In　this　paper,　we　investigate　the　B　&　eacute;nard　problem　of　the　incompressible　viscoelastic　fluids　heated　from　below　in　a　three-dimensional　periodic　cell,　and　establish　the　global　(-in-time)　existence　result　of　unique　strong　solutions　whenever　the　elasticity　coefficient　is　sufficiently　large　relative　to　both　norms　(of　energy　space　of　solutions)　of　the　initial　velocity　and　the　initial　perturbation　temperature.　Our　new　result　mathematically　verifies　that　the　elasticity　under　the　large　elasticity　coefficient　can　inhibit　the　thermal　instability　even　if　both　the　initial　velocity　and　the　initial　perturbation　temperature　are　large.　Moreover,　the　solutions　also　enjoy　the　exponential　decay-in-time.　In　addition,　using　the　method　of　vorticity　estimates,　we　further　derive　that　the　convergence　rate　of　the　nonlinear　system　towards　a　linearized　pressureless　problem,　as　either　time　or　elasticity　coefficient　approaches　infinity,　is　in　the　form　of　c　kappa-1.　Our　converge　rate　is　faster　compared　to　the　known　rate　c　kappa-12　first　found　by　Jiang-Jiang　in　[23].　(c)　2025　Elsevier　Inc.　All　rights　are　reserved,　including　those　for　text　and　data　mining,　AI　training,　and　similar　technologies.