Crossword Genius

Got temperature wearing hairpiece (7)

Ross

I believe the answer is:

twigged

I'm a little stuck... Click here to teach me more about this clue!

'got' is the definition.
(I've seen this before)

'temperature wearing hairpiece' is the wordplay.
I cannot quite understand how this works, but
'temperature' could be 't' (abbreviation) and 't' is found within the answer.
'hairpiece' could be 'wig' (wig is a kind of hairpiece) and 'wig' is present in the answer.
The remaining letters 'ged' is a valid word which might be clued in a way I don't understand.
This explanation may well be incorrect...

Can you help me to learn more?

(Other definitions for twigged that I've seen before include "Got wise" , "understood" , "like the elder" , "caught on" , "Got the point" .)

I've seen this clue in The Times.
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