The　early-warning　of　fire-induced　failure　of　structural　members　is　becoming　more　and　more　attractive　to　the　fire　department　since　it　can　provide　warning　signal　to　the　firefighters　at　the　scene　of　a　building　fire.　Temperature　is　a　type　of　easily-measured　parameter　in　fire　condition,　and　can　reflect　the　ultimate　state　of　structural　members　to　some　extent,　therefore　it　has　the　application　potential　to　indicate　the　failure　of　structural　members　in　fire.　The　traditional　critical　temperature　method　(CTM)　in　Eurocode　3　or　Chinese　standard　GB　51249-2017　has　been　widely　used　in　the　fire　safety　design　of　steel　members,　but　it　cannot　be　extended　to　the　early-warning　of　fire　-induced　failure　directly.　Based　on　the　traditional　CTM,　this　paper　presents　an　advanced　critical　temperature　method　for　simply-supported　H-shaped　steel　beams　under　different　fire　scenarios.　Finite　element　analysis　(FEA)　models　were　established　and　validated　to　investigate　the　critical　temperatures　of　H-shaped　steel　beams.　Based　on　the　numerical　analysis,　guidelines　for　confirming　the　positions　of　characteristic　temperature　points　(CTPs)　and　values　of　refined　critical　temperatures　(RCTs)　on　H-shaped　steel　beams　were　proposed,　and　parametric　analysis　results　indicated　that　the　longitudinal　fire　scenario,　perimeter　of　beam　section　and　beam　load　ratio　were　the　key　influencing　parameters.　Finally,　a　design　table　was　proposed　to　determine　the　positions　of　CTPs　and　values　of　RCTs　of　simply-supported　H-shaped　steel　beams　with　2-hour　fire　rating　time,　which　can　be　used　in　the　early　-warning　of　fire-induced　failure　directly.