This　paper　combines　functionally　graded　materials　(FGMs)　with　the　cable-stayed　beam　to　propose　a　cable-stayed　functionally　graded　beam　(CSFGB)　model.　The　influences　of　temperatures　on　nonlinear　behaviors　of　the　model　are　analyzed　when　one-to-two　internal　resonance　of　the　global　mode　(FGB)　and　the　local　mode　(cable)　is　triggered.　First,　the　governing　equations,　which　consider　thermal　effects,　are　derived　through　the　extended　Hamilton＇s　principle.　Thereafter,　the　modal　functions　are　obtained　based　on　the　boundary　conditions.　On　this　basis,　the　governing　equations　are　discretized　by　employing　Galerkin　discretization,　resulting　in　a　set　of　ordinary　differential　equations　(ODEs).　The　method　of　multiple　time　scales　is　then　applied　to　solve　these　ODEs　and　derive　the　modulation　equations.　Finally,　nonlinear　dynamic　behaviors　of　the　CSFGB　at　three　different　temperatures　are　analyzed.　The　results　show　that　as　the　temperature　decreases,　the　response　increases,　making　chaotic　motion　more　likely　to　occur.　Moreover,　the　distribution　of　FGMs　has　a　significant　impact　on　nonlinear　responses　of　the　system.　©　2025　Elsevier　Ltd