By comparing the genetic variation of Neanderthals in Western Europe from more than 50,000 years ago to analogous data from less than 50,000 years ago researchers have established that Neanderthals in Western Europe nearly went extinct before modern humans encountered them. Per the article:
"The fact that Neanderthals in Western Europe were nearly extinct, but then recovered long before they came into contact with modern humans came as a complete surprise to us," study co-author Love Dalén, associate professor at the Swedish Museum of Natural History in Stockholm, told Phys.org. "This indicates that the Neanderthals may have been more sensitive to the dramatic climate changes that took place in the last Ice Age than was previously thought."...."It may very well have been the case that the European Neanderthal populations were already demographically stressed when modern humans showed up on the scene."
Given this it would be interesting to see if people in warmer areas like India have more Neanderthal DNA than Western Europeans.