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 tha 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.