With this caveat in mind, we have investigated the change in probability of extreme weekly averaged temperature anomalies, in both winter and summer, from the first half-century (1901-1950) to the last half-century (1960-2009) of the 1901 to 2009 period. We have done this using two newly available global atmospheric reanalysis datasets (ERA-20C and 20CR-v2c) and large ensembles of global coupled climate model simulations of this period, plus very large ensembles of uncoupled atmospheric model simulations of our own. The results are revealing. In the tropics, the changes in the extreme warm and cold temperature probabilities are indeed generally consistent with those expected from the mean shift of the distribution. Outside the tropics, however, they are generally significantly inconsistent with the mean temperature shift, with many regions showing little or no change in the positive temperature extremes and in some instances even a decrease. In such regions, it is clear that the change in the temperature standard deviation is important. The discrepancies in the estimated extreme changes among the model simulations and observational datasets are also largely attributable to the discrepancies in their estimated changes of standard deviation.