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The resistance of thin-walled steel beams in fire is governed by a complex interaction between the buckling of the plates and the lateral-torsional buckling (LTB) of the member, combined with the temperature-induced reduction of steel properties. Besides, in many applications, steel beams are subjected to non-uniform thermal exposure which creates temperature gradients in the section. There is a lack of analytical design methods to capture the effects of temperature gradients on the structural response, which leads to overly conservative assumptions thwarting optimization efforts. This paper describes a study on the strength of thin-walled steel beams subjected to constant bending moment in the major-axis and thermal gradients through analytical and Machine Learning (ML) methods. A parametric heat transfer analysis is conducted to characterize the thermal gradients that develop under three-sided fire exposure. Nonlinear finite element simulations with shells are then used to generate the resistance dataset. Results show that the use of the Eurocode model with a uniform temperature taken as the hot flange temperature severely underestimate the moment strength with an R^2 of 0.61. The ML models, trained using physically defined features, are far superior to the Eurocode methods in predictive capacity. The ML-based models can be used to improve existing design methods for non-uniform temperature distributions.