I'm back from my trip to Spain and to answer my own question: lack of air conditioning wasn't an issue since there was almost no humidity. Yeah it was hot (in the 90's), but I remained dry. I just kept my windows open all the time but I drew down the shades during the day to keep the sun out--not that I stayed in my room much during the day anyway.
I felt safe leaving my belongings during the day. My room had a lockable closet but I still carried the passport etc in my money belt wherever I went.
Late at night (3am-ish) Calle de la Magdalena is kind of deserted but one block over, Calle Atocha has a good amount of people traffic. If you're uneasy about walking down a deserted street on the way to Hostal Numancia, then take C. Atocha, cut across at C. Canizares, turn right onto C. Magdalena and you'll be at the front door of the hostel.
It's on the fifth floor. If you take the stairs late at night when it's dark, just hit the light switch on the first floor and the lights on each level of the staircase turns on. Or you can take the elevator.
Here are a couple of pics to give you a better idea of what it's like here.
The "lobby"
The main hallway
One of the two bathrooms (always very clean)
Room number 12 (single)
View from my window at 3pm