To address the problem of axial thermal deformation induced by frictional heat generation in the dual-ball-screw feed system of heavy-load, long-stroke ultra-precision machine tools, as well as the resulting inter-axis synchronization error, this paper develops an indirect thermo-fluid-structural coupled thermal-performance model that incorporates the convective coupling "mutual insulation" effect between parallel ball screws. The study systematically analyzes the heat generation mechanisms associated with servo motor losses and frictional heating at angular contact ball bearings and ball screw nut pairs. It establishes thermal boundary conditions for natural convection, rotational convection, and forced convection, equivalently simplifies the heat generation from rolling contact, and refines the mesh in critical contact regions. On this basis, a built-in circulating cooling channel is designed, and a fluid–solid conjugate heat transfer approach is employed to compare non-cooled and cooled conditions. The experiments yielded temperature deviations below 5% at both monitored locations. For each feed axis, the difference between the predicted and measured screw-end elongation remained below 7%, supporting use of the model under the tested condition. Under cooled conditions, the maximum temperature of the ball screw nut decreases by approximately 23°C, and the maximum temperature of the bearing decreases by about 9.4°C. Additionally, the inter-axis thermal elongation difference narrows from 20.6μm to 11.3μm, resulting in a reduction of the thermally induced synchronization error by roughly 45.1%. The results indicate that the proposed model accurately captures the coupled heat transfer behavior of the dual ball screws, while the cooling channel effectively mitigates temperature rise and non-uniform thermal deformation, providing both theoretical and simulation-based foundations for the thermal design, constant-temperature control, and thermal error compensation of dual-ball-screw feed systems.