360 running hot…very hot

Yup, and previous picture showed the late model aluminum water pump on the engine, which is a passenger side inlet.
That puts both the inlet and outlet of the radiator on the passenger side.
It's likely a dual pass radiator like 92b said above. The OP made it sound like he bought it new, so he can verify. If it's not a dual pass, that'd be an awfully bad f-up for a 'new' radiator.