I looks like an auxiliary trans cooler.
It's mounted on right side of the cross member. (5.0L) It seems to be an inline auxiliary trans cooler between the transmission and the cooler in front of the radiator. It also has coolant lines attached that tee off of the overhead heater hoses. Thanks

 

Oil cooler

 

Factory Service Manual says it is a transmission fluid warmer.

 

Its the transmission fluid heat exchanger. It both warms and cools the fluid using engine coolant temp. My 15 for example doesnt have the front mount cooler, only that heat exchanger. 14-15 they eliminated the intenral thermostat of the trans and used this instead. 10spd trucks have both an exchanger and a thermostat

 

Great. Thanks to both of you for the diagram and explanation.
On another note, where is a good place to get the factory service manual? The Haynes manual isn't cutting it for me anymore.

 

Pretty sure you can get an electronic copy off evil-bay.

 

I checked out ebay, but I'm not sure which manuals are best. I don't want a "one size fits none". I'd like a factory make and model specific manual.

 

Here's where I got mine- I purchased the regular one with no links to the various sections from another, but I think the extra money spent on the "link" version is better:

https://www.factory-manuals.com/shop

Discussion on this forum here:
https://www.f150forum.com/f118/repai...n-ford-329736/

 

Thanks, reg, I'll check them out.