The computer models created by CRU are attempts to fit the historical temperature data statistically. Then they extrapolate the fit into the future.
Empirical models (logarithmic, polynomial, power series, or exponential) can be made to reproduce any amount of historical data (curve fitting). It is an exercise in mathematics to generate such equations by calculating numerical coefficients that have no real world relationships with the phenomenon being modeled (average temperature, or the Dow average for instance). Only a fool would would bet that the same model can predict the future as they do not represent cause and effect and therefore they can only reflect the past (data that was used to formulate them).
Regards,
GtG