Take a look at the original sentence again:
Sylvia shivered in her silk shirt, the difference
in temperature between the hot road and the cold library was extreme.
You chose to fix it the correct way:
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 the problem.