In recent years, observations have highlighted seasonal and interannual variability in rock glacier flow. Temperature forcing, through heat conduction, has been proposed as one of the key processes to explain these variations in kinematics. However, this mechanism has not yet been quantitatively assessed against real-world data. We present a 1-D numerical modelling approach that couples heat conduction to an empirically derived creep model for ice-rich frozen soils. We use this model to investigate the effect of thermal heat conduction on seasonal and interannual variability in rock glacier flow velocity. We compare the model results with borehole temperature data and surface velocity measurements from the PERMOS and PermaSense monitoring network available for the Swiss Alps. We further conduct a model sensitivity analysis in order to resolve the importance of the different model parameters. Using the prescribed empirically derived rheology and observed near-surface temperatures, we are able to model the correct order of magnitude of creep. However, both interannual and seasonal variability are underestimated by an order of magnitude, implying that heat conduction alone cannot explain the observed variations. Therefore, we conclude that non-conductive processes, likely linked to water availability, must dominate the short-term velocity signal.