Cyclones are a key element of extratropical weather and frequently lead to extreme events like wind storms and heavy precipitation. Understanding potential changes of cyclone frequency and intensity is thus essential for a proper assessment of climate change impacts. Here the behavior of extratropical cyclones under strongly varying climate conditions is investigated using idealized climate model simulations in an aquaplanet setup. A cyclone tracking algorithm is applied to assess various statistics of cyclone properties such as intensity, size, lifetime, displacement velocity, and deepening rates. In addition, a composite analysis of intense cyclones is performed. In general, the structure of extratropical cyclones in the idealized simulations is very robust, and changes in major cyclone characteristics are relatively small. Median cyclone intensity, measured in terms of minimum sea level pressure and lower-tropospheric relative vorticity, has a maximum in simulations with global mean temperature slightly warmer than present-day Earth, broadly consistent with the behavior of the eddy kinetic energy analyzed in previous studies. Maximum deepening rates along cyclone tracks behave similarly and are in agreement with linear quasigeostrophic growth rates if the effect of latent heat release on the stratification is taken into account. In contrast to moderate cyclones, the relative vorticity of intense cyclones continues to increase with warming to substantially higher temperatures, and this is associated with enhanced lower-tropospheric potential vorticity anomalies likely caused by increased diabatic heating. Moist processes may, therefore, lead to the further strengthening of intense cyclones in warmer climates even if cyclones weaken on average.