Review the original item:
Sylvia shivered in her silk shirt,
the difference in temperature between the hot road and the cold library
was extreme.
You chose the correct way to fix the error:
Sylvia shivered in her silk shirt,
for the difference in temperature between the hot road and the cold
library was extreme.
Sylvia shivered in her silk shirt is a main clause. The difference in temperature between the hot road and the cold library was extreme is a second main clause.
Using a comma and a coordinating conjunction like for is an excellent way to fix this comma splice.