There is no evidence that 20th Century climate change has the same cause as the medieval warm period. There is however strong evidence that it is largely caused by man-made emissions of greenhouse gases.

Even if the estimated peak temperature in the so-called medieval warm period in southern Greenland is comparable with that of the mid 20th Century temperatures inthe same locality the argument  that this proves that 20th Century global warming has a natural cause has flawed logic. If the latter type of argument was true the following argument would also be true.  There were at least as many deaths from Black Death in the middle ages as in the Second World War so the latter deaths must have been caused by Black Death. Establishing that two measurements made about 1000 years apart are similar does not establish that they have the same cause.
  Besides, there is insufficient evidence to claim that the pattern of climate change in time and space during the medieval warm period is similar to that of climate change since 1750.  What is known so far suggests that the observed pattern during the medieval warm period is compatible with the hypothesis that it was caused by changes in Atlantic Ocean circulation. It is widely held that changes in ocean circulation may have an impact on global climate at regional scales and changes in the equatorial Pacific circulation (El Nino) do have a small but detectable effect on global mean temperature. However there is no evidence that changes in circulation are the cause of recent global warming while the evidence outlined below strongly indicates that  man-made emissions are the primary and principal cause of this.