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The objective of this study is to evaluate to what extent the CMIP5 climate model simulations of the climate of the twentieth century can represent observed warm monthly temperature extremes under a changing environment. The biases and spatial patterns of 2-, 10-, 25-, 50- and 100-year return levels of the annual maxima of monthly mean temperature (hereafter, annual temperature maxima) from CMIP5 simulations are compared with those of Climatic Research Unit (CRU) observational data considered under a non-stationary assumption. The results show that CMIP5 climate models collectively underestimate the mean annual maxima over arid and semi-arid regions that are most subject to severe heat waves and droughts. Furthermore, the results indicate that most climate models tend to underestimate the historical annual temperature maxima over the United States and Greenland, while generally disagreeing in their simulations over cold regions. Return level analysis shows that with respect to the spatial patterns of the annual temperature maxima, there are good agreements between the CRU observations and most CMIP5 simulations. However, the magnitudes of the simulated annual temperature maxima differ substantially across individual models. Discrepancies are generally larger over higher latitudes and cold regions.