Additional temperature stresses in continuously welded rails (CWRs) are caused by track/bridge interaction (TBI) due to thermal actions. Exceeding permissible stresses in CWRs on the bridge can lead to track buckling or rail cracking, compromising the safety of railway traffic. The main aim of the conducted study is to determine the effects of the key parameters such as rail cross-sectional area, track longitudinal resistance, bridge expansion length, and longitudinal stiffness of the fixed bridge support on the reduction of additional temperature stresses in CWRs on steel truss railway bridges. To quantify the effects of these parameters, two steel railway bridges with CWRs and the maximum expansion lengths according to UIC Code 774-3 were analyzed: (1) simply supported truss bridge with expansion length of 60 m and (2) continuous truss bridge with expansion lengths of 2 × 60 m. According to the obtained results, the track longitudinal resistance had the most significant impact on additional temperature stresses in CWRs, leading to their reduction of up to 72%. The bridge expansion length and the rail cross-sectional area led to reductions of up to 25% and up to 18%, respectively. Considering the deformation criteria of TBI, the longitudinal stiffness of the fixed bridge support had a minor effect on the reduction of additional temperature stresses in CWRs.