first of all are you sure that all the radiators are clean and working properly and they re not blocked? there are 2 intercoolers in front of front wheels and more in the middle as you might know.. if they re blocked by bugs, plate, or a pipe etc. it can cause overheating easily.. its not a season in NY to cause overheating.. generally since the ones in front of the tires, can get dirty easily cause front wheels sprey water behind those coolers.. after some time intercoolers back part becomes like it covered by dried mud.. you can grow a flower over there..
another easy thing to start is to check the ratio of coolant.. it needs to be 50/50 water and BMW blue coolant.. to measure that, you can check it or make it checked by a small gadget that measures the sugar level etc in the coolant.. other one you can taste it by yourself it shouldnt be that sweet..
since winter is coming, you ll need at least like -20 but not more resistant to freezing.. if you have something like -30 you can take some of the coolant out and add the same amount of distilled water.. and bleed the system properly.. at the same point another question arises.. are you sure that there is no air in the cooling system? it can happen between season changes and how frequent you drive the car.. and it can get worse by time if it didnt bleed properly since you re saying you were having problems recently.. there might be some air in the system.. these are the 3 easy things to check and they re pretty important.. if all of these are ok, you probably have a bigger issue..
but above all S63 do burn some oil if you dont warm the oil properly before pushing.. if you re doing it, you need to stop it as well.. you ll lose less oil like that..