[exDemMom]

Consider the case of the Plains Indians and the Buffalo herds. The herds grew to huge proportions but the Indians never had populations high enough to put a dent in the population.

Those animals have fairly high reproductive rates. Some of the large animals produce few young, and it takes a long time for the young to mature to reproductive age. Elephants, for example, gestate for two years and become sexually mature at age 14. Some of the megafauna (which were much larger than elephants) probably had even longer cycles. With such a slow reproductive rate, it would not take much hunting to disrupt the viability of the herd. Couple that with the climate changes--large body mass makes dissipating heat difficult--and they could not survive.

[GladesGuru]

“Couple that with the climate changes—large body mass makes dissipating heat difficult—and they could not survive.”

Considering that these animals had survived numerous glacial periods prior to the anthropogenic predation period, arguably, heat stress would not be an extinction factor.

[rdcbn]

If you go back and look at the fossil records, you can see very substantial changes and comparatively rapid in the physical characteristics of the megafauna in response to rapid climate changes in the highly unstable warming period of the ice age.

It is very likely that the inability to adapt to rapid and radical climate swings had more to with the extinctions than human predation.