That's a really warm "cool side" & I would guess that's possibly why he's looking to go somewhere else- or it could be just the "fresh air" that's carrying interesting scents from beyond.
To stop him from rubbing on the screen top, I'd remove those branches that allow him to reach it- he won't be able to, just by reaching upwards. It honestly doesn't appear to be a "rub" though.
Even without A/C, there's other ways you can offer him cooler temperatures if needed. For example: Keep a plastic bottle of water in the fridge, to exchange with one in the "cool" corner of his enclosure twice a day. Sometimes you just have to get creative- just always think "safety" too.
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