hot and cold tooth sensitivity for months after crown

Hot and cold sensitivity for that period of time following crown placement usually means that there is a nerve problem.  You will likely need a root canal if the pain does not subside soon.  If the sensitivity lingers for a period of time following having anything hot or cold you should go back to the endodontist and have the tooth reevaluated.  Good luck.  

Cold sensitivity is a very common occurrence after having dental work.  Much depends on how deep the cavity was, whether or not there was already a deep filling, any trauma that might have occurred to the tooth, etc.  All these things effect the health of the nerve inside the tooth.That being said, cold sensitivity after recent dentistry is oftentimes reversible and will go away with time, provided the tooth nerve is healthy.  Most of the time it goes away in a couple weeks, but sometimes it takes a couple months.If it progressively gets better, this is good, and I wouldn't worry about it.If it gets worse, get into your dentist.  You will probably need a root canal.If it does not get better after six months, then it is unlikely it will just get better with any more time.  In that case, again, best to see an endodontist and see if you need a root canal.