Could she give you a hot time? (4)

I believe the answer is:

june

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'time?' is the definition.
The definition and answer can be both related to time as well as being singular nouns.
Perhaps they are linked in a way I don't understand?

I can't explain the remainder of the clue.

Can you help me to learn more?

(Other definitions for june that I've seen before include "Sixth month" , "Spring/summer month" , "some time" , "Month after 14" , "Month named after Jupiter's wife" .)

I've seen this clue in the Evening Standard.

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