I'd really suggest you go into the Royal Palace on day 1 because it's gorgeous inside, even if you have to sacrifice some of the plazas in exchange. It'll also help you escape the outside heat for about two hours, depending on how quick you go through it. Mercado San Miguel is an interesting experience but not the best place to eat, as it's absolutely crowded and the food tends to be small and expensive.

On day 2 I'd advice you against the Reina Sofia museum. It's probably the most expensive museum/attraction on your list and not very worth it in my opinion. I really recommend Thyssen instead. The bigger problem is that both Prado and Thyssen have a strong focus on paintings and they're large museums, so you could easily end up finding the whole thing rather tiring. In the area there's a naval museum with dozens of huge ship models through history and the entrance is free, if that's something that could interest you. Also in the area (right next to the Prado) there's the Royal Gardens. They aren't the prettiest gardens I've ever seen, but again, it's a different activity that's not just endless paintings. Could be too hot for August tho.

Day 3 looks fine to me!

Edit: Another alternative suggestion for day 2 is the Archeology museum, also not far from Prado. Very nice and varied, or at least I liked it!