But there has not been cooling since. There was a period of very slight cooling about 1940 - 1980, followed by a greater increase of warming. The warming since 1980 has been about 0.4C, lots of room for a MWP.
0.4 C warming (subtracting the 0.1 to 0.15 degree measurement bias) is hardly unusual in the climate record. If you look at ANY of the raw data (untweaked) you will see one or two decades of dramatic warming all over the place including the LIA.