Yes to full gallon sized frozen water bottles! If you have 4, you can rotate them. A full gallon should last all day, and then has a full 24 hrs to freeze again. Growing up I lived in the central valley CA and it gets into triple digits in the summer… and I had buns outside.
Another thing that helps are these portable mister things that you attach to a hose. They are meant to be used by humans laying near the pool. You want to position so it’s not spraying directly on the bunny, but close enough to cool down the area. If the humidity is very high, it might not work that well though…..
The one we had was similar to this: https://www.lowes.com/pd/Orbit-ArizonaMist-Hose-Attachment/3733069
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The answers provided in this discussion are for general guideline purposes only. The information is not intended to diagnose or treat your pet. Seek the advice of your veterinarian or a qualified behaviorist.