recommended wire gauge

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Hi guys I've been making an amp using a 24 volts CT 12 amp transformer and what bothers me is the wire gauge stuff. I can get #22 and #20 stranded hook ups really easy but I cant get my hands on #14 below (yeah store near me sucks). I've been searching for wire gauge calculators or guide for dummies but I still think #14 below is overkill for non mains. Will #22 or #20 be sufficient and not overheat?
 
I'd like to know how you got 3W per foot.

What I did is divide the ohms per 1000ft by 1000 and multiply by 12A squared giving me ~1.5W. Can you point out what i did wrong? I would like to know which one is sufficient by your formula. thanks
 
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