I own a Chevy Volt, and it’s great. But I don’t think the battery is going to power my A/C for more than an hour.

Chevy Volt according to Wikipedia has something like 16.5 kWh.

I don’t know how big your house/flat is and for how much power your AC unit is rated for, but it should be enough for at least 3-5 hours under a full load for a rather powerful multi split AC unit.

If you keep in mind that AC doesn’t draw full power to keep an already cool room cool, your car might be just enough to keep the AC running through the night or majority of daylight hours.

The smarter move would be during an emergency to get everybody into the Volt and let it cool that smaller space. It won’t be as comfortable, but the battery would likely get you through the whole night at a decent temperature.