We had about 2 weeks of >40 C. All the hives survived though I know of a lot of people who lost stingless beehives. Here are the DPI recommendations regarding chalkbrood. http://www.daff.qld.gov.au/animal-industries/bees/diseases-and-pests/chalkbrood
It does mention high and low temperatures which can draw bees away from the brood, as well as other causes of stress.
Most of my hives are situated for morning sun as are yours. A bit of sun is a good idea for SHB control. One of my hives is under a tree's shade all day and it has had the biggest bearding of them all, and a couple have no shelter but are doing fine. The entrance is shaded the hottest part of the day.
I'm not an expert in thermodynamics, but someone in our club uses a fan inside the hive and monitors the temperature and has had high honey yields. Stingless bee experts have recommended using wet towels over the hives in those extremes of heat. Some people chock the lid open a bit. Usually in queensland we use the migratory lids with vent holes back and front. Usually folks take away the bit of plastic or whatever you put on top of your frames in summer, though that can lead to comb building in the lid. I don't know anything about screened bottom boards and haven't seen them used in these parts, so I can't advise about that. I would like to know the pros and cons. Some people put a lump of iron or something on top of the hive held down with a brick for a little shade in summer as well as protection from the rain. I wouldn't move your hives out into full sun if I were you. A little shelter wouldn't hurt. But checking the strength of your hive is more important as the chalkbrood may not be related to the heat or humidity.
Let us know how it goes.