There was time during the age of dinosaurs when the polar regions were ice free. The earth was obviously much warmer but a run-away greenhouse effect did not occur.
This was most likely because the continents were so configured that ocean currents more adequately transfered heat around the globe. And The particulate dust from volcanic activity (more active back then) accumulated in the stratosphere, reflecting solar heat and light back into space.
One reason creatures of immense size such as dinosaurs were able to evolve is the oxygen requirements for the respiration and metabolism for such massive bodies were present in the atmosphere during this period.
Similarly, the fossil record indicates vegetation size was much greater during this period than today due to the higher amount of CO2.
This atmosphere would have to have greater percentage composition of oxygen (for dinosaurs) and CO2 (for greenhouse affect and greater plant biomass) or a much denser atmosphere or both.
What was the density of the atmosphere back then either in terms of air pressure at today's sea level and standard temperature Or In kg/square meter at STP (Standard Temperature and Pressure)?
What were the percentages of O2 and CO2?