The 'models' project future climate. Every paleo data set that covers the periods of the MWP and LIA (which is pretty much all of them) includes all the data from those periods, so your statement are both false and astonishingly ill informed. 

As to the paleo record, there are multiple reconstructions using entirely different data sets that all agree that the MWP was very much cooler than today. Moreover, there is no credible data that supports the global impact of such an event, and lots that shows the opposite.