I was on a hike in July during a full moon and those who were sleeping in open air (no tent or bivy bag) struggled to sleep through the night due to the moonlight.
This was in the North West of Australia, so daytime maximums were around 35C. It was too warm at night to zip your tent or bivy closed, so where possible you would try to position yourself so that you could shield yourself from the moonlight during the night.
There were quite a few afternoon nappers in the group until the moon waned a little by the second week.