How long does the sensitivity last after the tooth bone grafting?

The graft probably fell out of the socket and now the socket is filling in on its own. Sensitivity to temperature changes is usually a result of the gum receding around the tooth that is retained in front of the area where the extraction took place. As such, the root is now exposed and open to the environment. It will heal with time. You should have the implant places in 4-6 months after extraction 

The gum tissue may look like it is not completely healed but chances are at 2 months the wound is sealed over although the surface may be a little irregular.  If you are sure that it is incompletely healed, I would suggest that you see your surgeon right away to make sure there is no bone exposed which would suggest necrosis or dead bone.  The sensitivity may just be coming from an adjacent tooth.