The impact of the El Niño-Southern Oscillation (ENSO) on temperature extremes is examined in both observations and coupled climate model simulations. HadEX2, a newly developed observed gridded dataset of climate extremes indices shows marked contrasts in seasonal composites of the monthly maximum value of daily maximum temperature during the cold and warm phases of ENSO. Extreme maximum temperatures are significantly cooler over Australia, southern Asia, Canada and South Africa during strong La Niña events compared to El Niño events and significantly warmer over the contiguous United States and southern South America. Two climate models are contrasted for their ability to capture these relationships given their very different simulations of ENSO. While both models capture some aspects of the observed patterns, the fidelity of the ENSO simulation appears to be crucial for simulating the magnitude and sign of the extreme maximum temperature relationships. The impact of future climate change on these patterns is also investigated.