Functionally　gradient　material　(FGM)　in　service　often　experience　temperature　variations　that　can　affect　the　propagation　characteristics　of　guided　waves.　This　investigation　aims　to　study　the　propagation　of　thermoelastic　guided　waves　in　the　FGM　plate.　A　computational　method　for　the　state　vector　and　Legendre　polynomials　hybrid　approach,　which　is　proposed　based　on　the　Green-Nagdhi　theory　of　thermoelasticity.　The　heat　conduction　equation　is　introduced　into　the　governing　equations,　and　optimized　using　univariate　nonlinear　regression　for　arbitrary　gradient　distributions　of　the　material　components.　To　study　their　dispersion　characteristics,　a　non-hierarchical　calculation　for　the　dispersion　curves　of　FGM　plates　versus　temperature　is　realized.　In　addition,　a　frequency　domain　simulation　model　is　developed　and　compared　with　theoretical　data　to　evaluate　the　accuracy　and　feasibility　of　the　proposed　theory.　Then,　the　influence　of　Legendre　orthogonal　polynomial　cut-off　order　on　dispersion　curve　convergence　is　investigated.　Subsequently,　the　shift　of　the　gradient　index　and　temperature　variation　on　the　fundamental　mode　in　dispersion　curve　is　analyzed.　The　results　indicate　that　changes　in　both　gradient　index　and　temperature　lead　to　a　systematic　shift　in　the　phase　velocity　of　fundamental　modes　in　the　low　frequency　range.　Meanwhile,　anti-symmetric　modes　exhibit　higher　sensitivity.　On　this　basis,　the　study　can　provide　theoretical　support　for　the　acoustic　non-destructive　characterization　of　FGM　plates　versus　temperature.