Exactly how hot are we talking, temp outside? According to numerous sites I've googled, Cayugas do best around the 70 dg temp area, as temps get higher, they can struggle. Mine is able to handle up to about 100 dg outside with minimal fuss...but that took time. She gradually acclimated to our very intense summer temps (up to 108dg!). Initially, open mouth breathing and fluffing out her feathers, wings slightly positioned away from sides...classic overheating signs. She was much less interested in interacting with her WH "sister", and spent most of her time in the kiddie pool.
If she has something caught in the throat, agreed that offering a treat in a deep water container and/or massaging the throat has worked for my WH in the past....she's a very fast eater and sometimes gets ahead of herself. Though in these instances, whatever was stuck in there moved down in minutes with a little help from me.
If you see other signs of heat stress that I described above: vitamins and electrolytes in her water, frozen ice blocks in most frequented water bowls (I freeze water in cool whip containers), and spraying down areas she hangs out in, midday, are good ways to help her cool. Some suggest frozen 2 liter soda bottles placed in pen though neither of my girls will actually lay near them, but worth a try! Side note: if our kiddie pool, water dishes, or feed station are in even slightly unshaded areas on hot days, my girl won't go near them.