My book on evolution, "Darwin's Ghost" by Steve Jones, tells us that ... "The first members of our species, Homo sapiens, arose about a hundred and fifty thousand years ago ..." and ... "Although Neanderthals, at first sight so similar to modern humans, were once placed on the last rung before mankind, fossil DNA hints that they might not even be on the same ladder. Their mitochrondial genes are quite distinct from our own. They were not the ancestors of human genes but followed a separate path. For mitochondria, at least, Neanderthals and ourselves split half a million years ago."
Quotes come from pages 322 and 323 of Jones' book.
Even 13 years ago Jones’ opinion was not supported by the single mtDNA comparison available at that time, which involved fewer than 400 base pairs out of a presumed 16,000+ in the Heidelbergensis specimen when alive. That wasn’t in accord with the morphological similarities even in 2001 (and the study was done years before that), and a more complete picture has emerged with nuclear DNA (and that’s from Neandertal specimens rather than a single Heidelbergensis specimen).