Going through a hot hive is not too bad, so don't worry if you catch it late. Just separate the boxes onto separate bottom boards and spread the entrances away from the original entrance so the grumpy foragers are split. (If you are using 10frame deeps you may want to split them more, such as into Nucs.) then 9 days later go through and cull queen cells. The one with the queen will be obvious. If you still can't find her divide it again and repeat. You can requeen the new Nucs or combine them or.... So many possibilities!
When I get hot colonies I keep them small in the spring, pull brood as often as needed to keep them from raising drones, until I can requeen with better stock. This way I don't spend money on a queen early, I get extra brood where I want it, the hot colony draws me some more comb, and i dont get mean drones in my dca's. The only thing I don't get out of them is honey and genetics. The one is not a loss and the other I make up for elsewhere in the apiary....
So in your situation, since they are strong, I would suggest splitting it up. If they are gentle enough you could shake all the bees into the bottom (so the queen is there and put the half the brood above a queen excluder. Then the next day you can pull splits off the top (to add brood to other colonies if you don't have a queen or cells available). Then split the remaining frames until you find the queen as above.
If they are very hot I find it can sometimes be difficult to requeen as they are picky. If they are not so hot you can just requeen and get a honey crop off them. But I would try to keep them small so they don't raise drones, until you get a nicer queen in there.
Good luck!