A　cable-stayed　functionally　graded　beam　(CSFGB)　model　is　proposed　for　the　first　time　to　study　nonlinear　behaviors　of　the　system　exposed　to　extreme　temperatures.　To　this　end,　the　in-plane　one-to-one　internal　resonance　between　the　global　mode　(FGB＇s　mode)　and　the　local　mode　(cable＇s　mode)　is　explored　under　the　condition　of　external　primary　resonance.　First,　governing　differential　equations　of　the　system　considering　temperature　effects　are　derived　by　using　Hamilton＇s　principle.　To　obtain　the　modal　function　of　the　FGB,　the　in-plane　eigenvalue　problem　is　solved　through　the　separation-of-variables　method.　Subsequently,　ordinary　differential　equations　(ODEs)　are　yielded　according　to　Galerkin　discretization.　The　method　of　multiple　time　scales　is　then　applied　to　deal　with　the　ODEs　and　derive　the　modulation　equations.　Based　on　the　above　theoretical　solutions,　the　frequency-/force-response　curves　at　three　different　temperatures　are　delineated　via　Newton-Raphson　method　and　the　continuation　of　fixed　points.　Meanwhile,　the　time　histories　and　phase　portraits　are　also　provided　by　directly　integrating　the　ODEs.　The　results　show　that　temperature　changes　have　a　significant　influence　on　nonlinear　characteristics　of　the　system.　©　2024　Elsevier　Ltd