My multitudes of rabbits were on water bottles through the summers for 10 years and I never had one not drink from a bottle because it was hot out. If a rabbit quits drinking from a bottle because the rabbit is hot then it is because the rabbit is overheated and will not drink because it is sick and probably to the point of dehydration that it does not want to move to the bottle or make the effort to drink. A rabbit that is overheated will not move to go drink from a crock any more than it would move for the bottle. If a rabbit gets to this point you can put a shallow dish of water right in front of them so they can just drop their head and drink to help them get liquid into their system since it is an easy way to drink for the exhausted rabbit. This problem is not however caused by water bottles, it is caused by excessive heat factors. Rabbits at fairs are usually forced into hot buildings with little ventilation or into tents that gather heat in the sun. A healthy rabbit that is not forced to be in an overheated situation will happily drink from a bottle all year long as long as the water in the bottle flows. So if your birds are in adequate shelters that are not kept way too warm for them they should never have a problem drinking from water bottles in the summer.
As an aside, I did find that the rabbits were quite talented at dumping water crocks of any size and weight unless they were securely fastened to the cage, like a locking crock, not just something wired there. Bottles are easier to manage and stay cleaner. It's always important to make sure your animals are drinking well from whatever source you give them, crock or bottle.
