Understanding changes in temperature extremes in a warmer climate is of great importance for society and for ecosystem functioning due to potentially severe impacts of such extreme events. In this study, temperature extremes defined by the Expert Team on Climate Change Detection and Indices (ETCCDI) from CMIP5 models are evaluated by comparison with homogenized gridded observations at 0.5° resolution across the Tibetan Plateau (TP) for 1961–2005. Using statistical metrics, the models have been ranked in terms of their ability to reproduce similar patterns in extreme events to the observations. Four CMIP5 models have good performance (BNU-ESM, HadGEM2-ES, CCSM4, CanESM2) and are used to create an optimal model ensemble (OME). Most temperature extreme indices in the OME are closer to the observations than in an ensemble using all models. Best performance is given for threshold temperature indices and extreme/absolute value indices are slightly less well modelled. Thus the choice of model in the OME seems to have more influences on temperature extreme indices based on thresholds. There is no significant correlation between elevation and modelled bias of the extreme indices for both the optimal/all model ensembles. Furthermore, the minimum temperature (Tmin) is significanlty positive correlations with the longwave radiation and cloud variables, respectively, but the Tmax fails to find the correlation with the shortwave radiation and cloud variables. This suggests that the cloud–radiation differences influence the Tmin in each CMIP5 model to some extent, and result in the temperature extremes based on Tmin.