Would "root grown into sinus", cause pain when exposed to cold or hot liquid.

This sounds to me exactly like what Dr. Maddahi proposed when he said "incomplete root canal' First of all, your root did not grow into your sinus. If your root was growing still (which its not) it would just slowly push your sinus membrane. Even if it did puncture the sinus (which it didn't unless he jammed the gutta percha filler wayyy through the end of the tooth) you would have different symptoms other than cold sensitivity. 
Most of the time (not always) those upper molars have 4 (or more) canals. It is not uncommon for a dentist to miss a certain canal, usually a canal called the MB2, leaving the nerve intact in that canal. AKA incomplete root canal. 
As Dr. Maddahi also said, it could be a tooth next to it. It's often hard for the patient to tell. 
If it is an incomplete root canal, try not to be upset with your dentist. It is a common issue. Those little MB2 canals are sometimes really really hard to find (and not always there in the first place) particularly without a microscope and/or cone beam ct image. 
Your doc will likely do a couple clinical tests to determine which is the issue. Good luck! 

Hi:On the root canal tooth you should not have pain to hot or cold.  Most of the back molars’s roots are in the sinus.  Either there is incomplete root canal or the pain is coming from the adjacent tooth.Best,Dr. Maddahi