Paint — something making dog ill? (9)

I believe the answer is:

distemper

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'paint' is the definition.
(distempering is a kind of painting)

I cannot understand how the remainder of the clue works.

Can you help me to learn more?

(Other definitions for distemper that I've seen before include "problem with dogs" , "Canine ailment - whitewash" , "Paint; animal disease" , "Paint for walls; disease" , "that's bad for kennels" .)

I've seen this clue in The Times.

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