You could look at the model simulations that were carried out as part of the Coupled Model Intercomparison Project Phase 5 (CMIP5) (http://cmip-pcmdi.llnl.gov/cmip5/). In particular, the "last millenium" experiment was completed by several modelling groups and covers a period of 1000 years (from 850 to 1850). The data is freely available. It's not 2k , but could 1k be enough for your purpose?