There are two types of sensitivity that can commonly experienced after a crown is cemented. One is sensitivity to biting pressure and the other is sensitivity to cold (and or hot) liquids. If a patient is experiencing either of these after a permanent crown is placed, then probably the best thing to do is to let their dentist know.
Sensitivity after a permanent crown is placed is not that uncommon. If a patient reports sensitivity to me, I check their bite, since a high bite can be irritating to the ligaments holding a tooth and can even cause pulpal sensitivity. A patient should be able to close there mouth comfortably without feeling any pain. If when they close their mouth (without chewing any food) they experience pain from a new crown, the bite should be adjusted.
If a patient can comfortably close their mouths, but does experience pain on heavy chewing, I usually ask them to wait and see if the pain gets better with time. A crown cementation can sometimes irritate the pulp and with time this irritation can diminish. This can take months to go away and if a patient is willing, its usually best to wait. If I see them at their next recall, the tooth is still sensitive to chewing or when drinking cold liquids, I take a radiograph and if nopathology is evident, I usually try to get the patient to wait longer, since the only real other options are to perform a root canal on the tooth or to cut off the crown and place a temporary crown with a sedative filling. Which of these I would choose, if I feel the need to treat the tooth, is dependent on whether I believe the pulp has a reversible or irreversible pulpitis.
Deciding whether a pulpitis is reversible is not always easy, but the prior history of the tooth has a lot to do with the decision. If a tooth was assymptomatic prior to me working on it initially, I am more likely to choose to remove a crown and place a temporary. If a tooth had a pre-existing crack in it or was symptomatic prior to me preparing it for a crown, I am more likely to recommend the patient visiting an endodontist and have a root canal done through the crown.
I feel that the pulp is still vital and not infected, there is usually no harm in watchful waiting, since with enough time sensitive crowned teeth can calm down. I explain this to my patient and if the symptoms are bearable we often wait for the symptoms to slowly go away. If the symptoms are worsening instead, we can always choose the root canal option.