From Science Alert:
Researchers have also hypothesized that climate change could have played a role in the extinction of Homo species. In a new study, published in the journal One Earth, a multidisciplinary team of scientists from Italy, the United Kingdom, and Brazil make the case that this factor was the major driver in the extinction of other hominins.
The authors believe the findings could serve as a warning as humanity faces human-made climate change today. "Even the brain powerhouse in the animal kingdom, [the Homo genus], cannot survive climate change when it gets too extreme," says paleontologist Pasquale Raia, of the University of Naples Federico II, one of the study's authors. "People should mind that, given the current mayhem we are causing."
Indeed, so have earlier periods of gradual warming led to mass extinctions..?
For three of the five extinct species - H. erectus, H. heidelbergensis, and H. neanderthalensis - a sudden, strong change in climate occurred on the planet just before these species died out. Climes became colder for all three, drier for H. heildelbergensis and Neanderthals, and wetter for H. erectus. According to Raia, the change in temperature was roughly 4 to 5 degrees Celsius, on yearly averages.
I'll take that as a 'no'. When they say "change in temperatures" they must mean "fall in temperatures" (Ice Ages are indisputably bad for humanity). If extinctions had coincided with increases, you can be sure they would have mentioned it.