Mine seemed to do just fine when the temperature spiked at 30C ((86 F), but that was for a a few days only (I lost a Botia kubotai). I kept them at 82 F for quite some time before moving them to the tank I have now, which sits at 78F most of the time. You may want to make sure you have extra aeration, particularly at night. I know they get oxygen from air that they get from the surface as well , but it may not be a bad idea at night when the plants respirate as well. I'm not sure how active corys are at night.
My Corydoras sterbai breeders have survived 4 summers where the temperature never dropped below 86*F. It gets hot and stays that way where i live, I can only keep and breed fish that are heat tolerant due to the hot summers.
I prefer keeping them between 80-82*F. and to stimulate spawning i temporarily add enough cold water to drop their tank temp to 75*F then allow it to rise back to the low 80's.
Although I have kept C. sterbai with Discus i now prefer to leave Corys out of Discus tanks and use Hypancistrus spp or Peckoltia sp L134 instead. They thrive in warm water and on the same foods I feed Discus. An adult Pleco of either genera is equivalent in clean up power as several Corys. I think Discus temperatures are a little too warm for most Corys if you take a long term view.
I breed both so I have had plenty of opportunities to gauge how they do at different temperatures.