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 wanted to fix it this way:
Sylvia shivered in her silk shirt,
because the difference in temperature between the hot road and the
cold library was extreme.
Because, a subordinate conjunction, would fix the problem in the original sentence if there wasn't a comma coming before it.
When a subordinate clause follows a main clause, you rarely use punctuation to connect the two.
You might want to consult the rules for fixing comma splices and fused sentences.