No sensitivity with acrylic temporary cap but cold sensation after putting zirconia cap?

This should not happen. Sensitivity indicates exposed tooth surface. If sensitivity does not go after 7 days. Visit dentist

Hi:
You should go back to your dentist to make sure the bite on the crown is ok and there is no clenching or grinding pressure on the crown.
Best,
Dr. Maddahi

Sometimes the cementation process can cause irritation to the nerve that takes a few days to calm down. Sometimes a tooth needs a root canal after having a crown placed. Give it a couple of weeks to get better. If at any point it gets worse, you need to see your dentist.