What The... Cho-ah?!

Readers of this blog might remember a story about mook vocabulary. The word "mook" was used for the basis of what the usual mook has to say, with various expletives thrown in. Anyone who begins to understand Korean (and Korean profanity) realizes sooner or later that it's fairly widespread among the population - even the kids.
Last winter, Flint and I added "cho-ah," the Korean word for cold, to the average mook conversation. It was, and is, their habit to constantly comment on the cold, whether it was to say, "It's cold," "I'm cold," "They're cold," "It's so fucking cold," etc., etc., etc.
I wondered, as winter turned to spring, what the mooks would say instead of "cho-ah." Would it be "tta-ttu," (warm)? Or "i-go," (hot)?
No, I have learned, they still say "cho-ah."
What the kimchi?
The hagwon where I work has an ancient air conditioning system that barely stays ahead of the heat and humidity. When the clasroom is full of 10-12 students, things can become... uncomfortable.
There is one room that is equipped with an extra wall unit, but I'm only in there twice a week. My favourite days to teach.
And the teacher's room gets pretty cool, as the teachers are not there during class. During break, it's a nice oasis for me, but every Korean teacher who walks in says "cho-ah," as soon as they feel the A/C hit them.
It's like it's still winter for them.
The room with the extra A/C unit gets positively chilly. If I crank it, even I begin to feel uncomfortable. I try to keep it at a point where both myself and the Koreans aren't distracted by the temperature, but I'm beginning to think this is impossible.
Arms will get withdrawn into t-shirts, so it looks like I'm teaching a class of amputees.
There's always at least one kid who mutters "cho-ah." Sometimes they'll say, "Alan, cold!" to which I reply, "No, I'm not."
Never let an opportunity go by to either teach them proper English, or torture them.