From time to time I encounter a doll with a warped head or digit. It is unclear how these things happen, but some of the likely scenarios is being smashed in storage or by a child, or exposed to heat and warping. In highly damaged dolls that come to me, it's nice there is no expectation as they are already in dire states as they are, so anything is an improvement. The good news is a lot can be fixed with heat so sharing a couple scenarios.
1) Skinny head - A doll came to me that looked likeshe had her head squeezed in a vice and was almost fish like with her eyes googling rather close together and her head shape looking rather squished. There was nothing inside the head to push it out. The fix on this was to get a nice big pot of water and boil it and then add the entire head. This head was rooted but bald so it wasn't going to hold any water, so I just kept flipping it around and around in the pot to ensure the whole head was hot. I used a pair of tongs and a large towel to fish the head out of the pot and set it on top of the towel as that water was hot! Using a pair of kitchen gloves, I stuffed the head full of empty plastic grocery bags and packed it tight and then let it cool. Once the head was cool, I removed all the grocery bags and the head was miraculously not pinched looking any more.
2) Flat arm - A doll came to me with a pinched arm, another issue where maybe something heavy was set on it or the arm was caught in a door lol. Since it was just an arm, and on this doll it did not easily come unattached, I used a blow dryer to heat the vinyl and then pinched it in the opposite directions, squeezing it from front and back so that the sides puffed out each time I did that. It did not take long to go back to it's original shape and then I just let it cool to set it.
3) Uneven neck plate - This is common on American Girl dolls where you remove the head and set it on a table and it wobbles because the vinyl neck portion is not flat. I do like to fix this issue because when stuffing the doll crooked vinyl can make the head lean, especially if you are stuffing that doll packed. For this issue I use the blow dryer once again until the vinyl is soft and heated. Then I put the head on an even table surface and press the neck portion down with my fingers. I hold it there until the vinyl cools, then it is set and flat.
4) Uneven eye holes - In changing eyes, sometimes it is possible to overstretch the vinyl trying to get it in if you don't have the right angle. Once the eye is in, if you see one eye hole bigger than the other, or both, it's a simple fix. Using the blow dryer method (without face-ups), re-heat the eye areas and pop the eyes out. Keep heating the eye sockets and using your hands pinch the sides of the head and from top to chin and the eye sockets will start to naturally go back to their original shape. Re-insert your eyes.
Surprisingly, most imperfections and distorted parts can be fixed by simply reheating the vinyl until it's soft and squeezing or reshaping and simply letting it re-cool.