When my nine year old was a baby and developed cradle cap, the warm olive oil treatment worked beautifully and the problem was resolved.
Fast forward to now, when my four month old developed severe cradle cap that spread down his forehead, into his eyebrows and down the sides of his face - NOTHING worked, and if something seemed to maybe help, it was only a short term solution as the crusting came right back. He was just the crustiest baby, it was horrible. He felt like sand paper and I think it bothered him because he would rub and scratch at his little face and head and sometimes leave scratches if his nails got too long.
The list of things we tried include: olive oil, sweet almond oil, coconut oil, jojoba oil, California Baby Calendula Cream, Weleda Calendula cream wash, tea tree oil, apple cider vinegar, baking soda, Selsun Blue, Head and Shoulders for sebhorreic dermatitis, an antifungal cream, and I'm sure a couple other things I can't think of right now. And of course then after his bath I'd have to take a baby brush and using the edge of the bristles, gently chip away at the flakes which took f-o-r-e-v-e-r. We ruined two baby brushes this way.
What finally 'cured' him was this baby shampoo called Mustela Foaming Shampoo For Newborns. I read about it several places online and decided to order some as a last resort. It wasn't cheap, or organic, or even natural at all, and it wasn't an overnight miracle, but a few weeks later his cradle cap was gone. His little head and face are soft and beautiful - can't even tell how awful it had been. I like that it's a foam because I had to really rub some into his eyebrows and it didn't run (it's tear-free but I don't want chemicals in his little eyes, it's bad enough I put it on his skin). I still use one squirt of the foam on his head in his bath at night (or any spots that look like they're trying to sneak back), and then when I get him out, while his head is still wet, I slather on a generous amount of the California Baby Calendula Cream (the thick kind that comes in that little tub, not the lotion in the bottle). This has been the winning combination for us.
But if you aren't dealing with an extremely persistent case I would definitely try to stick with more natural ingredients.