In this study, after validating the numerical simulation procedures, a three-dimensional model of a regular steel moment-resisting frame equipped with buckling-restrained braces (BRBs) was developed using Abaqus. A coupled displacement-thermal analysis was conducted on the frame under fire exposure following cyclic lateral loading. The effects of fire temperature, loading amplitude, and BRB geometric parameters on the frame's behavior were investigated. Results showed that increasing the fire temperature applied to the bottom-story columns and braces (from 777°C to 1067°C) raised the lateral force, bending moment, and rotation of the frame during fire exposure after cyclic loading. This increase highlights the sensitivity of steel moment frames (including those with BRBs) to fire temperature, especially at higher temperatures. Furthermore, under various fire temperatures, raising the cyclic lateral loading amplitude from 30 mm to 60 mm led to significant increases in lateral force (60%), bending moment (60%), and rotation (116%) during fire exposure. This demonstrates the high sensitivity of frame behavior to fire temperature at large loading amplitudes. Finally, reducing the BRB core thickness from 6 mm to 2 mm (particularly from 6 mm to 4 mm) under different fire temperatures decreased lateral force (67%), bending moment (67%), and rotation (56%) during fire exposure. This reduction indicates the strong sensitivity of BRB behavior, and consequently of the braced steel moment frame, to fire temperature and BRB geometric parameters, especially core thickness.