I wouldn't worry excessively about the transmission cooler with the DSG. Eventhough it is an automatic gear selection and clutch engagement it has no torque converter that is the greatest contributor to heat in an "automatic" transmission.
The pump and fluid only provide gear selection and clutch engagement through the Magatronic valve.
The heat build up towing should be little if any greater than a manual transmission. That lack of heat build up is why the thing is almost as efficeint as a manual transmission.
The computer clutch engagement is probably better than 99 % of the manual drivers can do. Of course the manual drivers would dissagree!
I have seen ratings on european sites that rate the DSG higher than the manual transmission.
I think the British VW site gives 75KG tow bar weight and 1500KG towing limits (With trailer brekes). The limiting factor seems to be the trailer breaking rather than the load rating.
Towing capacity from UKTOWING = 1889 lbs. for the 2009 Sportwagen TDI.
VW specs for the JSW:
Manual and DSG with brakes 1500 KG
Manual unbraked 740 KG.
DSG unbraked 750 KG.
Tongue (both) weight 75 KG
All in all I think that it is no worry for towing 750 KG (1650 lbs.) witout brakes and
the limit of 1500 KG. (3300 lbs) with brakes would give some comfort about the towing ability of the setup.
This is for the Golf variant (JSW).
The NEw Golf is rated 630 manual (unbraked) 1500 (braked)
640 DSG (unbraked) 1500 ( braked)
As you can see the limiting factor is more braking than towing capability as far as load rating on the drivetrain is concerned.
I guess it depends more on your comfort with the braking capabilities of the combination.
Obviously the JSW will tow more than the golf by 100 KG (220 lbs),but the drivetrain is the same.