Could an endocrine disorder cause sudden significant sweating (face, back of neck, chest) a few times a day not related to menopause or prednisone?

Yes: Do you have associated palpitation & HA? Have you checked blood pressure? Pheochromocytoma (a neuroendocrine tumor mostly involving adrenal gland) usually presents with sudden episodic symptoms of palpitation, severe perspiration especially involving upper half of body, headache and severe hypertension. Do you have hot flush? Talk to your DOC. You may need evaluation and physical examination.

Further testing.: Uncontrolled diabetes causes sweating. Increased thyroid function can increase sweating and the body temperature. Can be due to some medications used for anxiety or depression, specially in combination with other drugs . Infections or autoimmune disorders should be considered.

Many reasons: Including autonomic dysfunction. See your doctor soon.

Yes, but uncommon: Though the symptoms you describe could be related to an overactive thyroid or a super rare endocrine tumor like carcinoid or pheochromocytoma, the most likely thing is plain old, garden variety hot flashes. there are numerous other non endocrine possibilities. Please make and appointment to have your doc examine you and take a thorough history. That is the best place to start. Well wishes!