The 62F temperature is lower than some cories would like and is within the temperature range for other cories although a bit cool. A possible lesson for the future is that it is never a good idea to change things quickly in a tank except to remove poisons through water changes. Anything else that is done too quickly can have disastrous effects on the fish. Slow changes are always a better choice if all you have is an indication that something is not the way you want it. If the fish are obviously suffering, that might call for a bit more rapid change, but often things have developed within the fish's ability to cope and a rapid change can ruin the adaptation that they have achieved. You don't list the species of the cories, only their color, so we can't know whether the fish were actually in any trouble at all at 62F or not. An example is the aeneus cories, one of the more common albinos, that have a listed temperature range of 68F to 80F. At 62F they might be a bit uncomfortable but not really threatened by the low temperature. A slow rise to 70F would have not bothered them much. Most cories, sterbai are an exception, do not do well above about 75F so rapidly heating them even that high might pose a problem.
We seem to always remember that pH changes are a killer and soft to hard water or vice versa is difficult for a fish to deal with but we need to learn that temperature is also best changed slowly in most cases. I would make the exception when I find temperature so high the fish are having trouble getting enough oxygen, that would call for an immediate improvement to the point they were no longer gasping for air, then slow down.
