If it makes you feel any better, I have trouble with this too. "Can I turn down the air... I mean, reduce it... I mean, make it not so aggressively cold in here?"
"Can I turn up the air.. I mean, make it stronger... I mean..."
So you see, it's not easy to say whether you mean up or down in temperature or up or down in terms of output.
If you preface it with "It's a bit chilly" or "It's a bit warm" then it will be immediately clearly which one you mean, regardless of which word you use.
Student or Learner