。
She was shivering from the cold.
Literal
She [topic-は] coldness [by-で] was-shivering.
で here marks the cause of the action — the neutral, everyday choice for 'because of X,' broader than the literary に of cause that pairs specifically with involuntary triggers. ~ていた gives ongoing state in the past — she was in the middle of shivering, not just shivered once. The pair に vs. で for cause is a useful distinction worth carrying around: に tends to be reserved for involuntary inner triggers (cold, fear, joy that *make* you react from the inside), while で is broader and more external, marking circumstances or instruments. Many sentences accept either with subtle shifts in feel; this one with で reads as a plainer, more matter-of-fact account of the chill.