We investigate the relationship between the Last Glacial Maximum (LGM) and climate sensitivity across the PMIP2 multi-model ensemble of GCMs, and find a correlation between tropical temperature and climate sensitivity which is statistically significant and physically plausible. We use this relationship, together with the LGM temperature reconstruction of Annan and Hargreaves (2012), to generate estimates for the equilibrium climate sensitivity. We estimate the equilibrium climate sensitivity to be about 2.5°C with a high probability of being under 4°C, though these results are subject to several important caveats. The forthcoming PMIP3/CMIP5 models were not considered in this analysis, as very few LGM simulations are currently available from these models. We propose that these models will provide a useful validation of the correlation presented here.