Urban heat waves (UHWs) are strongly associated with socioeconomic impacts. Here, we use an urban climate emulator combined with large ensemble global climate simulations to show that, at the urban scale a large proportion of the variability results from the model structural uncertainty in projecting UHWs in the coming decades under climate change. Omission of this uncertainty would considerably underestimate the risk of UHW. Results show that, for cities in four high-stake regions - the Great Lakes of North America, Southern Europe, Central India, and North China - a virtually unlikely (0.01% probability) UHW projected by single-model ensembles is estimated by our model with probabilities of 23.73%, 4.24%, 1.56%, and 14.76% respectively in 2061-2070 under a high-emission scenario. Our findings suggest that for urban-scale extremes, policymakers and stakeholders will have to plan for larger uncertainties than what a single model predicts if decisions are informed based on urban climate simulations.