ProPhoto RGB has a white point of D50 and Adobe RGB has a white point of D65.  I don't see how you can convert from one to the other without getting a color cast if you use Absolute Colorimetric!  The very word "absolute" means you are not "converting" from one white point to another.  Not sure why Adobe's conversion doesn't do the same: they appear to be making a "relative" conversion when it should be absolute.  Simply put, you should get a warm cast if you do an absolute conversion from a D50 space to a D65 space because D50 light (from ProPhoto) will look warm when viewed at D65 (from Adobe).  If you don't want that absolute conversion, then use RC or Perceptual.

Why Adobe is doing it wrong, I'm not sure... I suspect they're taking a "non standard" approach and converting the white point because they know that Absolute Colorimetric intent is of little use to photographers DUE to the way it handles white point.  But I'll stick to the way I do it because doing it the Adobe way is wrong: it's no longer Absolute Colorimetric if you "scale" the white point!

Mike

Seems like I've found my solution here.
I'm scanning my patches one more time right now.

I've printed a file embed with Adobe RGB and with A. Colormetric, it came out really cold, specially in the paper based color in the image. And I think the reason is because my ICC file is generated wit D50 illuminant.

D65 -> D50 turns out cold

hopefully I'm right about it [crossing my fingers]

You should never be using absolute colorimetric unless you are producing a single (or several) color company logo or something like that where there are no neutral colors for the media to show through.  An example of that might be printing a Kodak logo where it is getting trimmed and you must get the shade of yellow exactly right and you don't care about media color.  Just remember: "absolute" colorimetric should "absolutely" never be used to print photos.    It is already known that PhotoShop's absolute colorimetric rendering doesn't work.  If you try to print a photo with absolute colorimetric in PhotoShop, it actually uses relative colorimetric.  At least that's what it appears to do.  One thing I know for sure: it doesn't work in PhotoShop.

Mike