The part number that Phill included, C6ZE-(8005)-F, on the radiator is as close to confirming the existence of the illusive "Desert Cooler" as any other. But that's where it stops. I tracked the "-F" and here's what I found.
Pic 1. The 60-68 Ford Car Parts (aka MPC) has no reference to a -F. That MPC version does not have the cross reference that the 75 edition has.
Pic 2. (A MS Word document with copied portions from an Adobe .pdf file) From the 75 edition of the MPC, shows a "C6ZE-8005-F" and its replacement, C3DZ-8005-K, but that leads back to the standard V8 replacement.
It exists, but was not supported for service.
Jim
On a whim, I checked the "Accessories" section of the 60-68 MPC but found no reference to any radiator. The same in the "Performance" section (but I did find that Ford sold "Lakes Pipes").