Two extreme temperature events (ETEs), both triggered by atmospheric blocking situations, were monitored by a pure rotational Raman lidar 20 km south of Paris. The first ETE lasted 6 days in late February 2018 with the onset of a cold wave surging from Siberia, and the second was a short heatwave that occurred at the end of July 2020. After calibration using simultaneous radiosoundings, lidar vertical profiles of temperature are derived with an uncertainty of less than 1 C within both the planetary boundary layer and the lower/middle free troposphere (~3/6 km above ground level [a.g.l.] for day/night), with a final vertical resolution of 50 m and a temporal resolution of 30 min. Such capabilities fulfil the observational requirements of the World Meteorological Organisation and contribute to fill a gap left behind by current operational instruments, which struggle to follow the diurnal cycle of the planetary boundary layer due to insufficient spatial and temporal resolutions in the low troposphere. These case studies allow to assess how such weather events are represented by numerical weather prediction modelling and whether they can be correctly observed by the Infrared Atmospheric Sounding Interferometer (IASI) spaceborne mission. Our results demonstrate that during these events both ECMWF reanalyses and forecasts are in overall very good accordance with lidar observations (correlation >0.9 in average). Still, they show warm biases (~1 C-2 C) compared with the lidar and improvable temperature field representation in the boundary layer. The radiances measured by IASI, assimilated in the operational model, do not capture temperature profiles adequately below ~2-3 km a.g.l., mainly due to the altitude location of its weighting functions. The bias computed against the lidar reaches 2 C during the heatwave and 4 C during the cold wave case in the first 2 km of the atmosphere, beyond expected errors found in the literature.