So-called hot droughts are seen as one of the very foreseeable extremes amid the faster-than-expected pace of global warming. In particular, the western part of North America has been pummeled by severe droughts due to a lack of precipitation as well as record-breaking hot temperatures. This study assesses the joint return period of drought severity and duration using the CORDEX-CORE simulations over the California domain. Six dynamically downscaled simulations with 25km resolution are analyzed for the historical (1956-2005) and future (2050-2099) periods, whose warming sensitivities differ based on three global climate models driving two regional climate models. Our focus is on estimating the joint probabilities of the drought duration and severity constructed from multiple drought indices such as the Palmer Drought Severity Index (with original temperature (PDSI) and its detrended counterpart (PDSI_detrended)) and Standardized Precipitation Index (SPI). Under the RCP8.5 scenario, an unprecedented level of droughts in terms of both duration and severity is likely to emerge only when the drought is characterized by PDSI. A comparison of PDSI and PDSI_detrended explicitly reveals that the occurrence of severe and prolonged drought is mainly attributed to the warming trend of temperature. Both PDSI_detrended and SPI, which do not incorporate the warming effect explicitly, barely differentiate the joint distributions from the historical and future simulations. Unlike the PDSI based on water budget, the SPI, based on solely accumulated precipitation, shows a loosely coupled joint structure between severity and duration of drought, with marked differences in their marginal distributions.