Observations of the lower stratospheric temperature over the last three decades show seasonal variations in tropical trends together with spatial patterns in southern high latitude trends in late winter-spring, with regions of cooling and warming of comparable magnitude. Neither aspect is reproduced in climate models used in the Intergovernmental Panel on Climate Change's Fourth Assessment Report (IPCC AR4). Here we show that stratosphere-resolving chemistry-climate models can produce these aspects of temperature trends. However, the seasonality of temperature trends can vary greatly among simulations of the same model, and even if one ensemble member reproduces the observed seasonality in trends there may be little agreement with observations for another member. The variability in trends among model ensemble members is related to differences in trends in wave activity propagating into the stratosphere. These results suggest that the seasonality of the observed temperature trends could be the result of natural variability as well as, or instead of, a response to external forcing, and that comparison with these trends may not be a robust test of climate models.