I'd select manual second on the shifter, keep the transfer case in low range, and if you're concerned about the trans fluid temp, look into adding a pusher fan for supplemental low-speed airflow. If things get warmer than you'd like, kick it up to neutral and hold the revs around 1500 or so for a little while to circulate the ATF and move a little air without putting a load on it, then back to business.
Biggest concern you'll probably have is the drag from ruts or mud -- and all that stop-start as the loader puts the hay rolls on and secures them. That would be a good time to put it in neutral or park and let it rev a little bit.