That linked thread was actually mine. I was able to reattach the steel cooler line to the top of the radiator. This winter I had the rubber coolant lines actually leaking. Because of the cold temperature I had a shop take care of this work.
The cooler lines out of the transmission run to a thermostatic valve that's located near the bottom of the radiator. The shop pulled the battery, battery tray, and the transmission support in order to replace the line that connects to the drivers side of the transmission.
That's what he told me he removed. I think he also removed the bottom bumper facia, and possibly the drivers side wheel well liner. I see a broken clip there.
It was $325 for parts and labor to do both of the lines. I think they come out together rather than trying to remove just one of those lines. I was thinking of trying to do this myself removing just one of the leaking lines. The one that went to the top of the trans.
After the owner of the shop looked at it, he said the labor was the same for one line, as it would be for both, the only difference being the parts. Therefore I had him replace the line that goes under the transmission support, behind the wheel liner to the side of the transmission.
You can see the connector in the wheel well with the drivers side wheel removed. However, I guess you can't snake the new line in without removing the battery and transmission support.
Good Luck-