Old news.
Climate model shows dual cause [of 20th century temperature trends]
And the models have improved since this was published:
By Looking Back, Scientists See a Bright Future for Climate Change Forecasting
"Chen and his colleagues report in the April 15 issue of the journal Nature that an improved climate model, known as LDEO5, for the first time predicted every major change in the temperature of the tropical Pacific Ocean over the past 150 years with up to two years of advance notice."
There is one problem with your request: the models use data that constitutes the boundary condition/starting point. The less accurate the starting point data, the less accurate the model will follow what actually happened. The further you go back in history, the data become less accurate, and therefore add more noise to the model reconstruction. So what you're really asking for is a model that makes accurate predictions based on bad data, and nobody really expects that to work.
I'm always grimly amused at how some wonderfully stable computer models (e.g. the ones the Club of Rome used in Limit to Growth) can be dead wrong despite being based on sound observations. But, they are still scientific theories in Popper's sense. (They just happen to have been falsified, and therefore shown to be wrong scientific theories.)
f.o.g. seems to not like my sociological point about scientific theories (whether good or bad) also becoming religious dogmas for secularists, but wants to deflect it by claiming the bad theories of the anthopogenic global warming crowd aren't scientific theories.