The biggest problem I've seen is that the bees can often get though the candy too fast (which is accelerated by those who insist in poking a hole in the candy). Baring any special conditions (drone layers, etc.), I'd expect a 95% success rate when queens are released in about 4-5 days. Most will be accepted faster than that depending on the conditions. When relying on the candy I've seen queens released as quickly as 18 hours and most hives will be though the candy far quicker than 4-5 days which is not good except in ideal conditions.
It doesn't seem to matter which style of cage is used, 3 hole, California, JZBZ, etc. While I generally get pretty good success just placing the cage, I get much better success leaving it for 4-5 days and doing a direct release if they aren't biting the cage. Or alternately putting tape over the candy for 2 days then removing it to allow then to be released normally.
A good honey flow and young bees can increase acceptance as can how long the new queen has been laying and how long she has been caged or banked. Lack of the former and other conditions will reduce acceptance and increase the time necessary for good results. I'm guessing your heat limited the flow and kept the old bees at home.
I do normally wait 24 hours before introducing queens myself with no noticeable problems.
-Tim