I disagree. A cooler is definitely required. The good news is that there is one installed on all X5 models with an automatic, from the factory, so no additional cooler is required. As Krunk says, you are fine. The cooler is thermostatically controlled. The thermostat is not the same as the engine coolant thermostat. This cooling system is one reason that the X5 transmissions don't tend to wear out (although they do tend to break). I don't know the thermostat setting, but someone with technical manuals may have the spec.

While I have never seen a GCWR published, there is certainly a maximum tow rating published by BMW, and there are limits published for maximum drop and reach for the hitch ball. There is also a braking requirement published for trailers over a certain weight. So I do think that BMW has considered towing, and isn't completely silent on the issue.

BMW also mention more frequent service requirements under the label of severe service in their maintenance recommendation (in my vehicles, not sure about the 2010 model), and heavy towing could certainly apply in that case.

Having said that, look up posts by withidl on this board. He regularly towed 8000+ pounds of Airstream with his E53, over the continental divide many times, and never had any transmission issues. I think the transmission does not have issues with overheating. It does have other issues, but I don't think they are impacted by towing.

But then, I'm not a cynic

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2007 X3 3.0si, 6 MT, Premium, White

Retired:
2008 535i, 6 MT, M Sport, Premium, Space Grey
2003 X5 3.0 Steptronic, Premium, Titanium Silver
2002 325xi 5 MT, Steel Grey
2004 Z4 3.0 Premium, Sport, SMG, Maldives Blue