Coping badly with heat, leading to disease (10)

I believe the answer is:

pathogenic

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'leading to disease' is the definition.
I can't judge whether this definition defines the answer.

'coping badly with heat' is the wordplay.
'badly with' indicates an anagram.
'coping' mixed up with 'heat' gives 'PATHOGENIC'.

Can you help me to learn more?

(Another definition for pathogenic that I've seen is " Causing disease".)

I've seen this clue in The Independent.

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