Polarly opposite connotations of 'head'?

Such aphorisms as 'Think With Your Head, Not Your Heart' connote positivity of the noun 'head', but such English words as heady and testy connote negativity. So why this clash and polarity of connotation?

Per Etymonline, the etymology of 'testy' involves French. Does French help to explain anything?

To "think with one's head" suggests the value of using logic; not the value of the head for all things.

"Heady" and "testy" both suggest emotion - something that goes to the head and prevents normal, logical thinking processes.

In circumstances where it may be a positive thing to think with one's head, it wouldn't necessarily be good to be "heady" or "testy."

Usage of the "head" as the "thinking end" of a person invites contrasting uses that emphasize good/clever/bad/dull or clear vs. distorted thinking. Hence polarities are formed in both positive and negative ways. As you probably know, there can be many forms of "Think With Your Head, Not With Your ______", and not all of them would be positive.