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We develop a new analytical and numerical approach, based on existing models, to describe the onset of lateral–torsional buckling (LTB) for simply supported thin-walled steel members. The profiles have uniform I cross-sections with variable lengths of the flanges, to describe also H cross-sections, they are prestressed by external tendons, and they are subjected to fire and various loadings. Our approach manages to update the value of the prestressing force, accounting for thermal and loads; the critical multipliers result from an eigenvalue problem obtained applying Galërkin’s approach to a system of nonlinear equilibrium equations. Our results are compared to buckling, steady state, and transient state analyses of a Finite Element Method (FEM) simulation, in which an original expression for an equivalent thermal expansion coefficient for the beam–tendon system that accounts for both mechanical and thermal strains is introduced. Our aim is to find estimates for the critical conditions with no geometric imperfections and accounting for the decay of material properties due to fire, thus providing limit values useful for conservative design. This approach can surpass others in the literature and in the existing technical norms.