Gauge rods (GRs) can improve the stability of the horizontal direction of the ballasted track structure and are an important component for strengthening the curve section. In order to investigate the influence of GRs on continuous welded rail (CWR) stability, a finite element CWR stability model considering track random irregularity was established. Taking CWR for heavy-haul railway with a curve radius of 400 m as an example, it was confirmed that the non-uniform irregularity of two rails for one track is the basis for function implementation of GRs. The influence of installation temperature, laying spacing and installation location of GRs on allowable temperature rise range (ATRR) of CWR was analyzed with the finite element CWR stability model. The results show that when the rail temperature variation is only considered, GRs can reduce rail lateral displacement caused by rail temperature force and improve CWR stability. Compared with the results without GRs, ATRR of CWR corresponding to the curve radius of 400–4000 m increase by 6.3%–9.6%. When the temperature of GRs and rails are consistent at all times, GRs can decrease ATRR of CWR. As the difference between installation temperature of GRs and stress-free temperature of CWR reduces, ATRR of CWR decreases significantly. When the difference is 10 °C, ATRR of CWR drops by 10.5 °C with a decrease of 17.9% compared to the results without GRs. The laying spacing and installation location of GRs have little effect on CWR stability. In order to guarantee the stability of CWR with GRs, the adverse effects of temperature change of GRs should be considered in the design of CWR. The installation temperature of GRs should be higher than the stress-free temperature of CWR, and the number of GRs should not be too large.