Are there any A/B test/ statistics results revealing whether using warm color buttons is generally better than cold color buttons in UI? (despite the concern for the theme color of the brand)
The answer to your question depends on context (that means A/B testing*) :
1) Color of the background and surrounding buttons
You want the call to action button to out-stand so really it is more the text displayed, contrast, size and style than the colors that are going to make a difference.
As a rule you can consider that the bigger the button less brighter has to be its colour.
2) Culture of the visitor
Color is not going to be interpreted the same way by different people. Typically red is a color hard to use : it can be very outstanding but might be frighting.
To answer your question : no, it will not be better for making call-to-action buttons in warm colors because you certainly cannot make it a rule.
To illustrate there is my favorite home page :
*A/B testing cannot give a general answer, just inputs for a specific layout and content