re:.Prescient, based on available information.
These were huge sons-of-a-gun. With healthy appetites. The herbivores ate so many plants that after a few million years of denuding the planet of vegetation, they were running out of food and began starving to death. However, these weakened, starving herbivores made easy meals for the carnivores who then got fat and lazy since they didn't have to chase their food anymore. It must have been like having a delicatessen on every street corner. (Sound like any species you know?) But it didn't last long.
Up to this point your theory sounds like a good extrapolation on the information to the general population.
If the plants did not grow as fast as they were eaten, then your assumption sounds reasonable.
The growing lack of vegetation caused global warming. Global warming is, according to current scientific theory, when the planet's temperature gradually warms up, thereby causing a greenhouse effect.
According to the information that I have, your assumption at this point is somewhat backwards.
According to the scientists, it is the greenhouse gasses that cause the global warming.
You could speculate that the carnivores ate all the herbivores and then pooped all over the place, that generated enough greenhouse gasses to warm up the atmosphere, when the atmosphere got too warm it expanded and some of it escaped into space, this expansion caused cooling of the atmosphere and the ice age was born freezing all the dinosaurs to death.
Since the global warming froze all the dinosaurs to death, then the same may happen to us, only this time we are the ones heating up the atmosphere until it becomes so cold that we can not survive anymore. :-)