Poor Pia...and you Dina! You just can't win for losing! Your a good mommy in making her not be sooo hot and now this! Well, atleast, it is easier to control the cold then hot! I bet her hair grows back pretty fast and that will give her some thickness (even if you keep it short).
How about satin...isn't it pretty warm too (like fleece)? I remember satin sheets (back in the day)

that seemed to be pretty warm. Satin, fleece and flannel.
How about if you put her clothing in the dryer before putting them on her? I think the flannel and fleece would hold in some of that heat for awhile.
I know since we cut Mojo done really short, we have had to keep clothing on him too...course, I am hot natured and HAVE to have the AC cranked up, but I have managed it on a higher setting to help Mojo!
That Pia, she's such a tiny girl......I just don't know what else you can do. The heating discs are nice, but I know that girl likes to be on the move...I just don't know.