Wow. I haven't visited this board in months, and when I drop by, there's a question I can answer. Cool.
I've stayed at Hotel Plaza Mayor twice and as I recall there is a small AC/Heater unit attached to the wall in the room. You can adjust with a little remote control if you can figure it out. You might want to ask the friendly staff for a quick lesson.
Otherwise the Hotel is great. The location is absolutely unbeatable, the staff is helpful, everything is clean, and the attached cafe is handy if not memorable. It's a bit more expensive than some of the budget hostals in the area, but a bargain by US standards.
When I was last there (March '01), Plaza Provincia was totally torn up for the construction of a traffic tunnel. It sapped some of the charm from the neighborhood, but I would stay there anyway.
Have fun,
Steve