Marine heatwaves (MHWs) and Cold Spells (marine cold spells (MCSs)) are events of extreme positive and negative temperature anomalies, that last 5 days or longer. These events have been diagnosed across oceans from sea surface temperatures (SSTs) and recognized to affect ecosystems' health worldwide. Some studies have focused on the extent, evolution, and drivers of specifically intense and long‐lasting regional MHW events. Although extreme temperature anomalies could lead to coral bleaching, mortality, and ecosystems' shift from healthy to barren reefs, no studies have focused on MHWs and MCSs in the Caribbean Sea. This study characterizes them in the Caribbean Sea, explores simultaneous thermal‐stress and coral response, and reveals prevailing environmental conditions during their occurrence. We use four decades of SSTs observed daily and a recently published database of worldwide coral bleaching events. We found bleaching events occurring simultaneously with both MCSs and MHWs, often with extreme events of mild intensity and typical duration. We find a positive long‐term trend in MHWs' frequency, consistent not only with global warming, but also with the Atlantic Meridional Mode. There is a clear seasonal signal with MHWs occurring more often in summer and MCSs in autumn‐winter. Our results suggest MHWs and MCSs development is related to El Niño/La Niña conditions, respectively. Finally, we identify intense extreme temperature events that span large areas as candidates for future studies on their dynamics. Our results are relevant for the development of MHWs and MCSs forecasts applied to conservation strategies and ecosystem‐based management of marine resources, particularly in reef systems.