Is it なか or うち? How about in set expressions like 心の中で思う as in 「私はとても幸運だわ」と彼女は心の中で思った。and how about 心の内？
心の中 is normally, and far more often, read as こころのなか.
I'd read it as こころのなか when it's used to mean "in(side) one's heart" "inside" "inwardly" or "silently", as in phrases like 「心の中でつぶやく」「心の中で自問する」 etc. So I'd read the 心の中 in 「私はとても幸運だわ」と彼女は心の中で思った as こころのなか.
心の中 can also be read as こころのうち.*
I'd read it as こころのうち when it's used to mean "one's heart" "one's feelings" "one's inner thought", as in phrases like 「心の中を明かす」「心の中を語る」「心の中を吐露する」 etc.
(You might find it more commonly written as 心の内 or 心のうち.)
*According to 明鏡国語辞典:
It's こころのなか. 中 is very rarely read as うち at least in modern Japanese, although some dictionaries seem to recognize such a reading.
心の内【うち】 is also acceptable in this context, but I feel 心の内 tends to be used more often when your true feeling is different from what you say or how you appear. In this case such a contrast is not important, so 心の中 is fine.