The steel sections are subjected to instability and buckling failure due to the rapid degradation of flexural rigidity under fire-loading conditions. The behavior of monosymmetric hot-rolled steel I-section beams are studied in this paper under uniform and non-uniform moment conditions. Validated finite element models in ABAQUS is used for parametric study, considering 1500 linear and non-linear simply supported beam models. Behavior of monosymmetric I-beams is analyzed under different uniform temperature conditions having shorter, intermediate, and longer spans with a height-to-width ratio greater than two (h/b > 2). The collapse of beams with longer span is not much affected by the non-linear material behavior. Only up to 17% increase from elastic capacity is observed for such beam under inelastic capacity. The interaction curves for the degree of monosymmetry and moment gradient are provided that can be used for estimating inelastic lateral-torsional buckling (LTB) capacities. Further, statistical analysis and comparison of FE-results with design predictions from Eurocode 3 part 1.2 showed that a single design buckling curve is insufficient in predicting the collapse capacity of hot-rolled beams under different loading conditions at elevated temperatures. Eurocode 3 part 1.2 generally provide highly conservative predictions at higher temperatures for beams under single curvature; however, it may provide unsafe results under double curvature for intermediate to shorter span beams.