The difference between Cool off and Pull in one's horns
When used as verbs, cool off means to decrease in temperature, activity, or temper, whereas pull in one's horns means to become less impassioned, aggressive, or argumentative.
check bellow for the other definitions of Cool off and Pull in one's horns
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Cool off as a verb (intransitive):
To decrease in temperature, activity, or temper.
Examples:
"You are getting a little too angry; you need to cool off."
"The metal will take about three hours to cool off after the molding."
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Cool off as a verb (transitive):
To cause to decrease in temperature, activity or temper.
Examples:
"At first he was very angry, but his friends managed to cool him off."
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Pull in one's horns as a verb (idiomatic):
To become less impassioned, aggressive, or argumentative; to exercise restraint; to yield or capitulate.