Resigned oneself, annoyed about once-treated cold (10)

I believe the answer is:

reconciled

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'resigned' is the definition.
('reconcile' can be a synonym of 'resign')

'annoyed about once-treated cold' is the wordplay.
'annoyed' becomes 'riled' ('rile' can be a synonym of 'annoy').
'about' means one lot of letters goes inside another.
'treated' indicates anagramming the letters.
'cold' becomes 'c' (eg on taps).
'once' anagrammed gives 'econ'.
'econ'+'c'='econc'
'riled' going around 'econc' is 'RECONCILED'.

'oneself' acts as a link.
This may not be correct. It may be part of another bit of the clue.

Can you help me to learn more?

(Another definition for reconciled that I've seen is " Friendly again after a quarrel".)

I've seen this clue in The Daily Express.

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