Motivated　by　the　stability　result　of　the　Rayleigh–Bénard　problem　in　a　fixed　slab　domain　in　Jiang　and　Liu　(Nonlinearity　33:1677–1704,　2020)　and　the　global-in-time　well-posedness　of　an　incompressible　viscoelastic　fluid　system　with　an　upper　free　boundary　in　Xu　et　al.　(Arch　Ration　Mech　Anal　208:753–803,　2013),　we　further　investigate　the　Rayleigh–Bénard　problem　for　an　incompressible　viscoelastic　fluid　in　a　three-dimensional　horizontally　periodic　domain　with　the　lower　fixed　boundary　and　with　the　upper　free　boundary.　By　a　careful　energy　method,　we　establish　an　explicit　stability　condition,　under　which　the　viscoelastic　Rayleigh–Bénard　problem　has　a　unique　global-in-time　solution　with　exponential　time-decay.　Our　result　presents　that　the　elasticity　can　inhibit　the　thermal　instability　for　sufficiently　large　elasticity　coefficient　κ.　©　2023,　The　Author(s),　under　exclusive　licence　to　Springer-Verlag　GmbH　Germany,　part　of　Springer　Nature.