I agree with all that's been posted here. Corys fare better the more there are, and I have found that this includes the species and combining species. I always try to get five or six minimum of a species; sometimes for various reasons this is not possible, but that is my goal. Beyond that, I keep mixed species in both of my tanks with corys, so the total number can be anywhere from 12 up to 40 or more, depending. In my 20 years of doing this, I have seen some species that prefer to stay relatively close together, and others that are very rarely in the same area of the 4 or 5-foot tank. There is certainly "safety in numbers" and that means less stress and healthier corys.
In your 3-foot tank, I would have 10-15 corys minimum; one species, two species, even three. The temperature issue is important, but with platy and cory you can be in the 75-77F range. Water parameters were also mentioned, and provided the extremes are not present you should be OK. Platy being livebearers will not be healthy in very soft and acidic water, and most corys will not do well in very hard water, and these are the extremes.
Byron.