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

I believe the answer is:
toasty
'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" .)
