In 2018 and 2019, heatwaves set all-time temperature records around the world and caused adverse effects on human health, agriculture, natural ecosystems, and infrastructure. Often, severe impacts relate to the joint spatial and temporal extent of the heatwaves, but most research so far focuses either on spatial or temporal attributes of heatwaves. Furthermore, sensitivity of heatwaves characteristics to the choice of the heatwave thresholds in a warming climate are rarely discussed. Here, we analyze the largest spatiotemporal moderate heatwaves—that is, three-dimensional (space-time) clusters of hot days—in simulations of global climate models. We use three different hazard thresholds to define a hot day: fixed thresholds (time-invariant climatological thresholds), seasonally moving thresholds based on changes in the summer means, and fully moving thresholds (hot days defined relative to the future climatology). We find a substantial increase of spatiotemporally contiguous moderate heatwaves with global warming using fixed thresholds, whereas changes for the other two hazard thresholds are much less pronounced. In particular, no or very little changes in the overall magnitude, spatial extent, and duration are detected when heatwaves are defined relative to the future climatology using a temporally fully moving threshold. This suggests a dominant contribution of thermodynamic compared to dynamic effects in global climate model simulations. The similarity between seasonally moving and fully moving thresholds indicates that seasonal mean warming alone can explain large parts of the warming of extremes. The strong sensitivity of simulated future heatwaves to hazard thresholds should be considered in the projections of potential future heat-related impacts.