Very nice idea and question! Of course, also climate scientists have already come up with this idea. And an other similar idea, which is to take the available data on the climate from say 100 years ago and run the simulation for the next 50 years, and compare the obtained result with the real data from 50 years ago. These are the "backcasting" and "hindcasting" approaches. One recent paper is this:
A. Carlsson-Kanyama, H. Carlsen, Barriers in municipal climate change adaptation: results from case studies using backcasting, Futures (2013): http://dx.doi.org/10.1016/j.futures.2013.02.008
But you may find some more popular descriptions on the links here, here or here. I hope you were looking for some references like this.