Some recent compilations of proxy data both on land and ocean (MARGO Project Members, 2009; Bartlein et al., 2011; Shakun et al., 2012), have provided a new opportunity for an improved assessment of the overall climatic state of the Last Glacial Maximum. In this paper, we combine these proxy data with the ensemble of structurally diverse state of the art climate models which participated in the PMIP2 project (Braconnot et al., 2007) to generate a spatially complete reconstruction of surface air (and sea surface) temperatures. We test a variety of approaches, and show that multiple linear regression performs well for this application. Our reconstruction is significantly different to and more accurate than previous approaches and we obtain an estimated global mean cooling of 4.0±0.8 C (95% CI).