I put one on my Camry, inline with the radiator (I tow a utility trailer sometimes). All that entailed was splicing into a line and mounting the unit forward of the A/C condensor.
One of the reasons that they run the tranny fluid into the radiator is to help maintain a constant operating tempreature. You don't want it over-cooling if you live in an area that gets cold. (Shouldn't be a problem for you in Arizona)
I don't know what harm that might do, but I do know that my car doesn't shift right when the tranny is cold (but then again, my tranny is slipping

)
Have you tried getting a radiator from a salvage yard?
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'88 Corolla, AE92 SR-5, 7A-FE swap/GT-S suspension
'87 Corolla, AE82 FX-16, 4A-GZE swap (autocrosser)
'03 Tundra 4X4 Access Cab, (FX tow vehicle/Home Depot runner)

Modification: Changing something to what you thought it should have been from the start!