In this work, we compare the rate of warming of summertime extreme temperatures (summer maximum value of daily maximum temperature; TXx) relative to the local mean (summer mean daily maximum temperature; TXm) over the Northern Hemisphere in observations and one set of large ensemble (LE) simulations. During the 1979-2021 historical period, observations and simulations show robust warming trends in both TXm and TXx almost everywhere in the Northern Hemisphere, except over the eastern U.S. where observations show a slight cooling trend in TXx, which may be a manifestation of internal variability. We find that the observed warming rate in TXx is significantly smaller than in TXm in North Africa, western North America, Siberia, and Eastern Asia, whereas the warming rate in TXx is significantly larger over the Eastern U.S. and central Europe. This observed geographical pattern is successfully reproduced by the vast majority of the LE members over the historical period, and is persistent (although less intense) in future climate projections over the 2051-2100 period. We also find that these relative warming patterns are mostly driven by the local hydroclimate conditions. TXx warms slower than TXm in the hyper-arid, arid, semi-arid and moist regions, where trends in the partitioning of the turbulent surface fluxes between the latent and sensible heat flux are similar during regular and extreme hot days. In contrast, TXx warms faster than TXm in dry-subhumid regions where the trends in the partitioning of the surface fluxes are significantly different between regular and extreme hot days, with a larger role of sensible heat flux during the extreme hot days.