Hot sun can damage the berries when they are black and ripening. Not while they are green or red. Sometimes a hot spell will come along when the berries are ripening and some will get ruined, but many will not. Especially since they don't all ripen at once and it's only the black ones getting ruined.
I happen to live in the Pacific Northwest where it doesn't generally get too hot and sunny, but sometimes it does. And for that very reason I own a large, white shade cloth. I think it's rated at 50% and the two times that I used it, it did an excellent job of protecting the berries. My berry trellis runs east-west so I only have to cover the south side.
I don't know your location or climate, but if it gets over 90 degrees and sunny when the berries are black, they are prone to "white druplets". Google for that if you don't know what it is.

I have had sun damage on more than one variety of blackberry when in the green/red stage. The small, tight-druplet stage is safe, but once the berries enlarge and show any color other than green, they are vulnerable to the sun.

The damage is more obvious to berries that are already black.

The shadecloth mentioned above is a good idea. If you end up using a dark-colored cloth, do not let it touch the fruit, those berries will burn.

How would I recognize sun damage? I am in central Alabama and the plants have morning sun thru 3 PM. I am getting large blackberrys 1" long from the Triple Crowns.
Paul

The most common sun damage is called "white druplet". Google for this and look at the images section provided.

Yes, random segments of the berry will turn pale and weep red juice. The berries are very sticky to handle. Amount of damage is proportional to intensity of the sun.

Blackberry UV (ultraviolet) damage is immediate and obvious, will plainly show by the next day after sun exposure.

Some berry varieties are immune, others are very susceptible.