hydraulic pump cooler, using trans cooler in radiator

I am in the process of installing the PSC hydro assist steering kit in my 1009 and I am considering adding a cooler. I am also considering adding a trans cooler.
my thought was:
Can I use the existing trans cooler in the radiator as the hydro cooler and just get one big trans cooler for the trans. The trans cooler connections on the radiator are right there where all of my steering parts are. this would eliminate some connections and keep from having multiple other coolers.

will the normal operating temp of the radiator be more than what the power steering/hydro system would normally be.

Has anyone done this?
Rich

You might want to check the pressure specs on the power steering. Seems like since the steering would be putting out a lot more pressure than the transmission which probably circulates trans oil at pretty low pressure up to cooler. If the power steering always flowed the same direction you could put cooler on the return side which should have pretty low pressure. I'd hate to have to buy or repair a radiator.