The number one overheating issue is mud in the radiator blocking air flow, it is not limited to the 1000, the 500s do it as well. I lead a lot of groups and have only ever had the issue once myself, 10 minutes with the pressure washer getting the radiator thoroughly clean makes all the difference in the world.
At our 2018 Takeover led a P500 group, had 2 machines that kept getting hot, I even towed out a CF Moto 800 SXS with 3 people inside, for 6 miles of muddy trails, my machine (P500) never got hot but people back in the group couldn't keep up without overheating towing nothing.
Point is, it is imperative to get the radiator clean after every ride, do that you likely won't have problems.