Heat waves (HWs) are among the most damaging climate extremes to human society. Climate models consistently project that HW frequency, severity, and duration will increase markedly over this century. For urban residents, the urban heat island (UHI) effect further exacerbates the heat stress resulting from HWs. Here we use a climate model to investigate the interactions between the UHI and HWs in 50 cities in the United States under current climate and future warming scenarios. We examine UHI 2m (defined as urban-rural difference in 2m-height air temperature) and UHI s (defined as urban-rural difference in radiative surface temperature). Our results show significant sensitivity of the interaction between UHI and HWs to local background climate and warming scenarios. Sensitivity also differs between daytime and nighttime. During daytime, cities in the temperate climate region show significant synergistic effects between UHI and HWs in current climate, with an average of 0.4 K higher UHI 2m or 2.8 K higher UHI s during HWs than during normal days. These synergistic effects, however, diminish in future warmer climates. In contrast, the daytime synergistic effects for cities in dry regions are insignificant in the current climate, but emerge in future climates. At night, the synergistic effects are similar across climate regions in the current climate, and are stronger in future climate scenarios. We use a biophysical factorization method to disentangle the mechanisms behind the interactions between UHI and HWs that explain the spatial-temporal patterns of the interactions. Results show that the difference in the increase of urban versus rural evaporation and enhanced anthropogenic heat emissions (air conditioning energy use) during HWs are key contributors to the synergistic effects during daytime. The contrast in water availability between urban and rural land plays an important role in determining the contribution of evaporation. At night, the enhanced release of stored and anthropogenic heat during HWs are the primary contributors to the synergistic effects.