The final draft of the EN version of part 1.1 of Eurocode 3 has introduced significant changes in the evaluation of the lateral-torsional buckling resistance of unrestrained beams at room temperature that reduce the over-conservative approach of ENV 1993-1-1 in the case of non-uniform bending. Numerical modelling of the lateral-torsional buckling of steel beams at elevated temperature has shown that the beam design curve from prEN 1993-1-2 is over-conservative for loadings other than uniform bending. In line with the safety format of the lateral-torsional buckling code provisions for cold design, an alternative proposal for rolled sections or equivalent welded sections subjected to fire is presented in this paper, that addresses the issue of the influence of the loading type on the resistance of the beam, achieving better agreement with the real behaviour while maintaining safety.