I’ve never read that the Neanderthal came out of Africa. Certainly the ancestors of Neanderthal had to but not the Neanderthals themselves.
Neanderthals were built for a cold climate not a hot African one.
Correct:
Year of Discovery: 1829History of Discovery:
Neanderthal 1 was the first specimen to be recognized as an early human fossil. When it was discovered in 1856 in Germany, scientists had never seen a specimen like it: the oval shaped skull with a low, receding forehead and distinct browridges, the thick, strong bones. In 1864, it became the first fossil hominin species to be named. Geologist William King suggested the name Homo neanderthalensis (Johanson and Edgar, 2006), after these fossils found in the Feldhofer Cave of the Neander Valley in Germany (tal—a modern form of thal—means “valley” in German). Several years after Neanderthal 1 was discovered, scientists realized that prior fossil discoveries—in 1829 at Engis, Belgium, and in 1848 at Forbes Quarry, Gibraltar—were also Neanderthals. Even though they weren’t recognized at the time, these two earlier discoveries were actually the first early human fossils ever found.
http://humanorigins.si.edu/evidence/human-fossils/species/homo-neanderthalensis
I agree, I think they were the result of a post migration evolution adaptation of a much much earlier migration.