In this study, a numerical analysis was conducted on aluminum alloy reticulated shells (AARSs) with gusset joints under fire conditions. First, a thermal-structural coupled analysis model of AARSs considering joint semi-rigidity was proposed and validated against room-temperature and fire tests. The proposed model can also be adopted to analyze the fire response of other reticulated structures with semi-rigid joints. Second, a parametric analysis was conducted based on the numerical model to explore the buckling behavior of K6 AARS with gusset joints under fire conditions. The results indicated that the span, height-to-span ratio, height of the supporting structure, and fire power influence the reduction factor of the buckling capacity of AARSs under fire conditions. In contrast, the reduction factor is independent of the number of element divisions, number of rings, span-to-thickness ratio, and support condition. Subsequently, practical design formulae for predicting the reduction factor of the buckling capacity of K6 AARSs were derived based on numerical analysis results and machine learning techniques to provide a rapid evaluation method. Finally, further numerical analyses were conducted to propose practical design suggestions, including the conditions of ignoring the ultimate bearing capacity analysis of K6 AARS and ignoring the radiative heat flux.