Some bottom rotting is developing on my peppers. I've seen similar stuff on tomatoes, but not yet on peppers. Is this blossom end rot, pepper edition?
The biggest cause of blossom end rot is not, in fact, calcium shortage in the soil - it's erratic watering. If the plant can't take up enough water for its needs regularly, it also cannot take up the calcium it needs. The weather cycle you describe is perfect for blossom end rot, if you didn't supplement sufficiently well with water when it was very hot and dry.
If you always have this problem, year after year, then its worth doing a soil test to check the calcium levels and supplement calcium if the levels are low. More info here: How To Stop Blossom End Rot.
Yes that is exactly what is occuring. I suggest you cleanse your soil with a little diluted dawn dish soap (antibacterial).
After this, crumple down or blend egg shells nice and finely. Lay them atop of the soil directly at the base of the plants. Add about a shot of milk to your soil as well, only once. Make sure your soil is not overly supple to water going straight through the soil and allowing it to dry too quickly and not staying saturated. When you add a ton of water to a plant constantly or after its been so dry, rot can occur.
Tomatoes are the worst when it comes down to water rot. But you have to make sure all the right strengthening nutrients are present.
I never have this issue, I make sure every single variant of pepper I have growing has egg shells. Whether they are in the soil or on top of it. Its old fashioned and is now commonly becoming apparent that it is sometimes quite needed. As for the milk, make sure it isn't a high quantity because of the sugar content. Thus a shot or 25ml will do.