Wildly rash, hot-headed and cruel (5)

I believe the answer is:

harsh

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'cruel' is the definition.
(synonyms)

'wildly rash hot-headed' is the wordplay.
'wildly' is an anagram indicator.
'hot-headed' becomes 'h' (this might be a standard abbreviation which I don't know about).
'rash' anagrammed gives 'hars'.
'hars'+'h'='HARSH'

'and' acts as a link.

Can you help me to learn more?

(Other definitions for harsh that I've seen before include "Not relenting" , "Guttural" , "Strident" , "Raucous - austere - bitter" , "Jarring" .)

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