Is temp crown supposed to be really sensitive or hurt?

Not suppose to..: ... But it can be. Talk to your treating dentist and tell them about your sensitivity.

May be: May be a little sore for a few days, but sensitivity should rapidly deminish. Most common cause of sensitivity is occlusal traumatized, crown may be infinitesimally too high, and a very quick occlusal adjustment will do wonders. May also be due to fracture or to a deep restoration. Call your Dentist for a reexamination.

No: No, it's most likely high on your bite or it could be the tooth it self. I'd advise you to call the office when it is open & have them look at it. In the meantime I'd stick to softer foods & take 600-800mg of IBU to control pain & inflammation

It shouldn't hurt: If you notice throbbing pain or sensitivity when you bite down, contact your dentist for evaluation.