Are both variants OK to talk about a change of weather we have had?
If I were a native speaker of English, I would never shut up. :-)
It's turned warm = It was previously cold and it has (probably recently) become warm.
It's turned out warm = We weren't sure what the weather would be like today but it has transpired that it is warm.
Remember - if you don't use correct capitalisation, punctuation and spacing, anything you write will be incorrect.
Informally, 'It's got warmer' is possible too.