This sentence doesn't need a comma after "heat":
The stuffy heat made him nauseous.
This needs one:
The muggy air, stuffy heat, made him nauseous.
Because we included "the muggy air."
Is this comma placement correct? What's the general rule?
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The example you give would be typical of speech, but not good written English. The phrase "stuffy heat" seems to have no function. It isn't linked to the rest of the sentence in any way.
You should write:
The muggy air and stuffy heat made him nauseous. (or nauseated if you want to use the prescribed adjective)
There are no commas required.
With a list of three or more items, then you separate with commas:
The muggy air, stuffy heat, and smell of dung made him nauseous.
(I've used an Oxford comma, though it is optional, and proscribed by some)
In speech you are more likely to get inserted phrases, not part of a list but just added in as an extra or to give an example. When transcribing speech you can use round brackets:
The muggy air (stuffy heat) made him nauseous.
Using parenthesis—or dashes—to represent this in writing is clearer than using commas.