Also, AC can be shifted. When power is cheap, use it to chill a tank of water or block of masonry, then use that coolness to reduce the AC load later. A tank of water can work just like a battery for HVAC.
Sort of. Away from the equator, days are longer in the summer, so one gets more total energy per day during the season when it's hottest. But hour-by-hour, the peak temperature usually happens later in the day (mid-afternoon) than the potential peak solar production (noon).
More pedantically, solar panels actually perform worse when they are hotter: https://www.thegreenage.co.uk/article/the-impact-of-temperat.... The ideal for solar power would be full sun and frigid cold. In the extreme (Andean mountain versus Australian outback) this difference in efficiency might be as large as 50% (+25% for the cold, -25% for the hot).
I agree with you that the "battery" doesn't necessarily need to store electricity, and that pre-cooling some large thermal mass might be better than a traditional battery.
Also, hot days happen everywhere at once, so you can't even borrow power from other grids, because they are likely just as in need of power as you are.