We study the performance of multiuser document prefetching in a two-tier heterogeneous wireless system. Mobility-aware prefetching was previously introduced to enhance the experience of a mobile user roaming between heterogeneous wireless access networks. However, an undesirable effect of multiple prefetching users is the potential for system instability due to the racing behavior between the document access delay and the user prefetching quantity. This phenomenon is particularly acute in the heterogeneous environment. We investigate into alleviating the system traffic load through prefetch thresholding, accounting for server queuing prioritization. We propose a novel analysis framework to evaluate the performance of the thresholding approach. Numerical and simulation results show that the proposed analysis is accurate for a wide variety of access, service, and mobility patterns. We further demonstrate that stability can be maintained even under heavy usage, providing both the same scalability as a non-prefetching system and the performance gain associated with prefetching.