People with acute illnesses and pre-existing conditions are particularly vulnerable to heat, making hospitals an area of high concern during heatwaves. Further, extreme heat impacts critical medical infrastructure due to increased patient admissions and impacts on workforce. This study assesses indoor heat occurrence and intensity in the University Medical Centre Freiburg, Germany based on measurements and data-driven climate simulations. Measurements were taken from May to September 2023 using a distributed sensor network in 60 rooms in 11 buildings. Measured air temperatures and physiologically equivalent temperatures are evaluated in terms of location, frequency, and intensity, as well as in relation to outdoor conditions, allowing for identification of vulnerable hospital structures and functions. Slight heat stress was most frequent and observed in all rooms, with 49 rooms showing additional occurrence of moderate and 17 rooms strong heat stress during summer 2023. Three heatwaves were identified as periods with high levels of heat stress and limited night-time cooling. Spatial hotspots were found in rooms without windows or air conditioning, located on higher floors, and predominantly in buildings constructed in 1950–1990. Measurements were combined with climate model data to project room-specific future indoor heat occurrence in all 60 rooms. All levels of heat stress are modelled to become more frequent and intense in rooms without air conditioning. Moderate heat stress or higher will increase on average by an additional 24 hours in 2020–2049 relative to 1990–2019. These findings call for immediate and widespread heat adaptation measures to ensure continued provision of critical medical infrastructure.