Most if not all automatic transmissions fluid/oil pumps work continuously except when in PARK. Many automatics route the transmission fluid thru the radiator for cooling or thru another cooler usually in front of the radiator. The lower the transmission fluid the longer the life of the transmission. (Of course if you live in Fairbanks, AK and it is minus 40F you need to warm the transmission fluid in neutral before moving. Yes al gore
Fairbanks still gets to minus 40.)
Good source for aftermarket auto trans coolers would be Summit Racing or Jegs.