Many kids do not like blankets, until older.
My son is 3 and still does not like a blanket on him.
My daughter, was that age but like it.
each kid being different.
As Jennifer S. mentioned, The calcium/magnesium intake, which helps sleep, does help many, even adults. "Animal Parade" make them for kids... liquid being more readily absorbed. I even take it myself sometimes... and many adults take it to reduce stress too, and to relax. It is not a sleep "aide" but like the ol' myth that drinking a warm cup of milk helps one to sleep... this is the same idea. There is something in milk that does help sleep, naturally. And some who lack magnesium (which aides calcium absorption and balances it), can benefit from it too.
But since your child just seems to have an issue with blankets on her... then I would just use footsie pajamas on her or Fleece pajamas (which are warmer).... and perhaps socks. Many kids, just do not like blankets, until they are older.
A child will NOT use a blanket if they do not want to. Ya can't 'make' them "like" a blanket. Like you can't make a horse drink water even if you drag them to the trough.
I know adults who kick off blankets too. Me, I HATED blankets on me when I was pregnant, both times. Its a preference.
And if she does not already have one, let her sleep with a "lovey" that she likes.
Oh some kids, even if "we" are cold, are not cold themselves. My daughter will get cold and bundle up. But my son, does not get cold and won't even want to wear long pajamas at night, even if it is cold.... its just him. So, gauge your daughter... maybe she could even be too warm/hot... and thus can't sleep?
All the best,
Susan