This is joint research with Peter Guttorp, University of Washington, Seattle, USA and Norwegian Computing Center, Oslo, Norway. While they may not be the most sensitive tools for assessing climate change, global mean temperatures are often used to assess how temperatures have changed over time. Different governmental and private climate groups construct estimates of global monthly or annual mean temperatures. Each estimate varies based on the raw data used (such as land-based temperature measurements, ship-based sea surface temperatures, data from buoys and floats) or the analytic methods used to create the global temperature estimate. Most of these groups also produce standard errors that are different for each estimate. In this talk we review how these groups construct their estimates, and propose a hierarchical time series modeling framework that produces a single estimate of global mean temperatures, that accounts for the uncertainty in the different estimates. Another source of information on the actual global mean temperature is climate models. Such models, run using historical forcings, can carry some information, and are also intended to model the actual global mean temperature. We thus study the role that climate model runs play as compared to our single estimate of global mean temperature.