This paper presents a study of the inelastic local buckling of flange outstands in thin-walled steel beams at elevated temperatures. A spline finite strip method of buckling analysis is modified in order to model the properties of the steel section at elevated temperatures, so that slenderness limits can be proposed. These limits are needed in describing the behaviour of members under fire loading, since the development of benign catenary action in a restrained beam that has received widespread research attention in fire engineering design is reliant on the formation of plastic hinges, and of the influence of local buckling on the formation of these hinges. A sensitivity analysis is undertaken in order to propose plasticity and yield slenderness limits at elevated temperature, and it is shown that these limits depend on the parameters describing the uniaxial stress–strain relationship at the elevated temperature. The local buckling temperature is predicted for two different boundary conditions for a flange outstand, and it is shown that at high temperatures the local buckling of the beam is highly significant in accelerating the favourable development of catenary action.