What might cause these black spots near the shoulders of these tomatoes? It had been in the mid 90s for ten days, and no rain. Heat stress? I tried to be consistent with water.

Bacterial spots can lead to marks like those, but it's also likely to have affected the foliage. There are a number of insects that tube feed from your fruit, causing black necrotic spots like that as well. In both cases the black is secondary rot from the initial damage to the skin and immediate tissues. Technically, poking the fruit with a pencil a couple weeks before it is ripe can do the same.

Unfortunately tomato plants are prone to a long list of fungal diseases. But those spots look like environmental damage to me like bruising.

Can you show a picture of the leaves?