Cooling is a habitability obligation here
Arizona law treats working cooling as essential in a rental, and an owner must repair a failure promptly. Tenants have specific remedies when that does not happen. That is a landlord-tenant matter rather than an insurance one, and knowing it is the first thing worth knowing.
Loss of use needs a covered peril
If a fire or a burst pipe makes the home uninhabitable, your policy pays to stay elsewhere. If the air conditioning simply failed, that is equipment breakdown on the owner’s side rather than an insured loss on yours, and loss of use generally does not respond.
Heat damages belongings too
Extended heat ruins electronics, instruments, candles, medicines and some furnishings. Whether that is a covered loss depends on the cause, and it is worth documenting the condition and the temperature rather than only the inconvenience.