Crossword Genius

Closed pen containing area that’s warm and cosy (6)

Ross

I believe the answer is:

toasty

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

'warm and cosy' is the definition.
I know nothing about this answer so I cannot tell whether this works.

'closed pen containing area' is the wordplay.
'closed' becomes 'to' (as in a door closed to).
'pen' becomes 'sty' (both can mean an animal enclosure).
'containing' means one lot of letters goes inside another.
'area' becomes 'a' (maths abbreviation).
'to'+'sty'='tosty'
'tosty' enclosing 'a' is 'TOASTY'.

'that's' is the link.

Can you help me to learn more?

(Other definitions for toasty that I've seen before include "Sandwich" , "Hot food" , "Cosily warm" , "nice and warm?" , "Pleasantly warm" .)

I've seen this clue in The Times.
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