Grammatically and meaning of "He has started feeling the heat of the chill"

He has started feeling the heat of the chill.

Is the above sentence grammatically correct and does it make some sense? We know that the word "heat" can be used in the following ways - "... in the heat of the moment" or "... feeling the heat".

So in the above sentence, is the writer trying to emphasize the cold weather?

It is grammatically sound but apparently doesn't make good sense, because of the opposition of heat and chill.

Informally, heat could refer to "intensity" and "undesirable amount of attention" and chill to "an uncomfortable and numbing sense of fear, dread, anxiety, or alarm" which might make sense, but in your "emphasize the cold weather" sense, heat doesn't work.

I won't say it's wrong. After all, Shakespeare wrote something similar:

O heavy lightness! Serious vanity!

Mis-shapen chaos of well-seeming forms!

Feather of lead, bright smoke, cold fire, sick health!

Romeo and Juliet

but if you're good enough to write like Shakespeare you really don't need our help!

I would say this can, in some ways, be a play on words. When I read it, it does sound a little clunky. On the other hand, John Lennon's book, "In His Own Write," is kind of similar.

Hope this helps (or knot).