What causes the transmission to pump fluid through the radiator?

'NO' (zero) fluid line pressure (4EAT transmission) is more than likely the fluid pump or pump drive shaft failure....Transmission fluid level extremely low....Completely restricted/blocked fluid filter.

A Automatic transmission is simply a hyd pump and is controlled my the solenoids and valve's in the valve body. Line pressure and circulation is determined by the PCM or BCM to control shift's. Cooling line pressure is most of the time close to zero when in park or neutral depending on the application. In low and rev at idle cooling line pressure is in between 65 - 110 PSI. If you checked the pressure in park you could very well see zero pressure but if you ran it thru the gears and still had no pressure then it's a small list of problems. Lack of fluid, valve body problem or the most common the hyd pump failed in the transmisson, either of the last 2 will require a trans rebuild. Good luck, Tim