You're assuming a lot here. The entire planetary biome was vastly different during the periods you mention. Your assertion hinges on the assumption that either phytoplankton were the primary source of atmospheric oxygen during these periods, or that modern phytoplankton can in fact withstand these changes in temperature and continue to make oxygen. Neither assumption seems to be well founded.
Of course Phytoplankton was always the biggest contributor to oxygen. Jurrasic was the age when flowering plants were first coming into being, to suggest that these plants could compete with plankton in oxygen production in any meaningful way seems absurd.
And more importantly what plankton we are taking about here isn't for me to address, it's something that would have been addressed in the paper were it worth anything. Are we talking about diatoms, cyanobacteria and dinoflagellates?
The biggest contributor to oxygen would be cyanobacteria, to think they can survive these billions of years and all these mass extinctions and temperature fluctuations and then stop working because of a 6 degree increase is also nonsensical.
