Here you find the basis for longer-term estimates of global temperatures:
Simulations of the last 1,000 years have been completed with several different models.
The models have been consistently wrong about their predictions. Thus, the basis is GIGO.
Also, they are only modelling the Northern Hemisphere (over landmass I presume, though the NASA propaganda piece doesn't make that clear).
Moreover, given that these have a resolution of 30 years ("smoothed with a filter") of averaging going on when they speculate about the 1400s or whenever, why not do the same with modern data (1990-present) when comparing it? When you realize that the "modern warming" is just ONE data point on such a scale, you realize how much the hype really is.