Could you perhaps make a "summer costume" for Snape that would look like it was multi-layered, but that would actually only be one or two layers? I've had to do that with a couple of outfits, and whether it works or not really depends on how authentic you wanna go with the outfit. I have a friend who cosplayed Darth Vader, and installed about a dozen battery-operated computer fans inside the costume, to circulate the air. Perhaps?