The common denominator is the radiator swap. When all is said and done air flow is extremely important. I'm thinking the fins are tighter together and not allowing as much air flow. It's correct that running it in 3rd shouldn't increase the trans temp, not by much anyway. Dropping it to 3rd increases the RPMs and puts more demand on the cooling system. A working system simply keeps up with the temperature regulation.
My Sierra had a custom grill cover on it when I bought it. Pretty cool looking. A few years ago we went to Gatlinburg. Very hot out. Around Indianapolis my trans temps were way higher than I was used to seeing, 220-230. It finally dawned on me about air flow. I removed the grill shell and it was back to 180 on flat land.