This is not uncommon frankly. We have mini-split A/C for our listings and they occasionally break. The offers you suggested all makes sense but you want to ask the guest what he/she wants. Some people are OK with the temperature with no A/C but some might find it unacceptable. If they are OK with the temperature, you may simply offer to cover some electricity or take 1-2 nights off the price. If they can't bear it, ask them to contact Airbnb to find other arrangement and cancel+refund the rest of the stay would be the most appropriate.
On the side, I'd suggest, if possible, to have a window or portable A/C on backup. When one breaks, you have the option to quickly deploy a window/portable unit so both you and the guest wouldn't have the headache. At the end of day it's also inconvenient for the guest to seek for other accommodations, as they are very tired and busy when travelling.