United does not have a general embargo for transporting cats
in summer. They don't accept short nosed dogs like boxers for
example. Of course if it is extremely hot at the origin or
connection airport, they can still decide on the day of departure
not to accept the animal. QA answer is probably correct if United
has a baggage agreement with them, which to my knowledge they
do and they transfer the bags to QA at IAD then the cats will be
transferred as well. You have to make sure to get a bag tag for
the cats to your final destination. I agree with the other posters
that it is not a good idea to take the cats if this is just a holiday.