The Earth was hot during this Mesozoic Era — from about 250 to 66 million years ago — the concentrations of CO2 in the atmosphere were up to 16 times higher than now, with temperatures six to nine degrees warmer than today. This was the time of the Triassic, Jurassic, and Cretaceous periods, dominated by reptiles (dinosaurs becoming the largest in average size during the Cretaceous) but with other marine, bird, mammal, insect and plant life evolving through the Jurassic and Cretaceous.
The Mesozoic Era began after the Permian/Triassic Extinction Event (likely driven by excessive volcanic activity in the form of huge areas of flood basalt in Siberia, with associated enormous releases of gases. The Mesozoic completed with the Cretaceous-Tertiary Extinction Event, which is coincident with a meteor impact in the Yucatan as well as Asian crustal plates staring to collide (continental drift), causing more volcanic activity, especially in the Indian Deccan plateau region (a lot more more basalt flow and gas). The resulting break in the food chain (plant life) is believed to have caused the extinction of the dinosaurs.
So, apart from acute events, the dinosaurs were far more adapted to the climate as was then but there was far more serious volcanic activity in general.