But global warming is a single weather change, likely a lot more severe than the continual changes that elevated sapiens (v. lucy) to sapiens (v. sapiens.)
Yes of course homo sapiens will figure this out – although at the same time the pressure to secure habitat and food could give rise to massive starvation, population movements, and war. Given that we have war-making abilities that can poison the planet and wipe people out in handfuls of millions with one bomb, what we call civilization is in serious danger. No of course sapiens will not disappear. After many dozens of centuries of successive small adaptations we may have “a new variety.”
But: bear in mind that a cloned, fully featured homo sapiens (v. neaderthal) would still be fully capable of interbreeding with homo sapiens (v. sapiens) and long-long-time-from-now homo sapiens (v. atomicus) would also be capable of interbreeding with v. sapiens, and doubtless also with v. neanderthal.
Species level changes absolutely take place, but the math says it happens only over spans of many thousands of generations. It’s been roughly one thousand since v. neanderthal, and close to two thousand since Australia lost contact with Asia. Evonne Goolagong, anyone? Fifty years ago she was a world tennis phenomenon, and of mixed aborigine/European parentage.