This thread has a lot of inaccurate and misleading "information." The fact is there are no species of Corydoras that should ever be kept at 80F/27C or any higher on a long-term basis. During specific disease treatments requiring warmer temperatures, or during temporary summer heat waves, are very, very different things, and the warm water is temporary. But absolutely never permanently by deliberation. This comes from "the" authority on Corydoradinae species, Ian Fuller.
Since I'm here, I will provide some info on the mentioned non-Corydoras fish temperature. The blue or common Ram, Mikrogeophagus ramirezi, must have temperatures above 27C/80F, preferably in the 84-86F/29-30C range. There are some other species that can do well with this, and Petitella bleheri and P. georgiae (Rummynose and False Rummynose), Paracheirodon axelrodi and P. simulans (Cardinasl Tetra and Green Neon Tetrsa, but definitely not the common Neon) are some. At 80-82/27-28C the Marble Hatchetfish Carnegiella strigata would be at the uppermost end of its "range" and thus better a bit lower. The same exactly applies to the Blue Acara.