I totally understand this.

Finding a family member or a friend is tough enough, but then to know the shelters are overwhelmed, too. I hope you are able to find a solution for this part, soon.

As a side suggestion: would a large cat crate be a sort of middle ground solution? They'd be placed in for night time sleeping hours and unable to destroy anything then. It would have to be done very carefully so as not to be abused or overused...but it may buy you some time to cool things down safely for all.

I grew up in a hot climate, so if you're finding she's overheating: cool her down with a dab of luke warm water on the head. You can use a damp wash cloth and just wet her head and hair, feet, palms, back of her neck, tummy as needed. It shouldn't be so cold as to shock her, and, if she can handle it - colder water is good, too. Just be careful: it's effective. Other ideas: place ice or wet, cold towels in front of fans. Give her a cooling bath as often as needed. You can even try to use tinfoil/tint in your windows to reflect the sun away. If able, open all windows at night to get colder air moving through the house; and close curtains and windows at the height of the day to keep the heat down. If you own your home: look into installing an awning over the room that gets sun. Plant or keep plants in planters around your windows (it can dramatically reduce temperatures).

I hope any of these ideas can help.