There are cheaper kits around. Have a better look.
OEM cooler is still available.
It's good preventative maintenance to replace them. They are the common things that cause issues that can be easily replaced. Consider them a mid life birthday. Once installed they should see the life of the box out.
Can be done trans in. It's a valve body out job. You'd need a new seperator plate as well. Plenty of ZF manuals around on the net to step through the replacement, check ball locations and torque specs.
OBD is preferred over a temp gun.
YepThatsIt on youtube has a couple good ZF videos