Global Warming Potentials (GWPs) are evaluated with historical temperature by applying them to convert historical CH4 and N2O emissions to equivalent CO2 emissions. Our GWP analysis is based on an inverse estimation using the Aggregated Carbon Cycle, Atmospheric Chemistry, and Climate Model (ACC2). We find that, for both CH4 and N2O, indices higher than the Kyoto GWPs (100-year time horizon) would reproduce better the historical temperature. The CH4 GWP provides a best fit to the historical temperature when it is calculated with a time horizon of 44 years. However, the N2O GWP does not approximate well the historical temperature with any time horizon. We introduce a new exchange metric, TEMperature Proxy index (TEMP), that is defined so that it provides a best fit to the temperature projection of a given period. By comparing GWPs and TEMPs, we find that the inability of the N2O GWP to reproduce the historical temperature is caused by the GWP calculation methodology in IPCC using simplifying assumptions for the background system dynamics and uncertain parameter estimations. Furthermore, our TEMP calculations demonstrate that indices have to be progressively updated upon the acquisition of new measurements and/or the advancement of our understanding of Earth system processes.