Nothing worse than a super hot hive that you can't even lift the lid off without getting hammered... my suggestion in that situation is conquer and divide. Basically move the hive away from it's current location, put down another box with (preferably) some drawn frames in it and let the field bees from the hive return to the old location. Then in the hive you will only have nurse bees and the Queen. You should be able to open them up fairly easily then and find the Queen. If not then a more drastic measure is to sieve them. I basically take an empty box, put it on the base and above that put a queen excluder and another box. Take each frame out of the hive and shake all of the bees on to the Queen excluder. Put the empty frames back in the hive... after you've shaken all of the frames and you have no bees left in the hive then put a lid on top of the box above the queen excluder then move the box, queen excluder and the box on top of that to beside your base. Put the hive with the brood frames back on the base and then pick up the queen excluder and top box (together) and put it back on top of the brood nest. You should have all of the nurse bees crawl through the excluder and next morning you should be able to lift the lid and see a queen sitting above your excluder. Then i would re-unite the brood nest and nurse bees with your field bees in the original hive location. Let them sit for a few hours and then introduce the queen cage directly above the centre of your brood nest. How many boxes do you currently have on the hive?
In regard Queens - I've tried a Ligurian and they didn't work for me - I personally prefer the dark queens but i figured that out by trial and error and what works for my area - it may be different for you. Virgin Queens from your other hives could potentially mate with drones from this hive you're looking at re-queeing... You could try raising a queen from one of your other hives but taking a queen from your other hives and introducing her in to the hive you want to re-queen could be risky if you don't have a queen cage. I would suggest purchasing a queen initially then when you have more experience try producing your own... the latest i would re-queen is autumn so long as you have a flow on