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The OP has stated that his transmission temperature is 31 degrees higher than his engine coolant temperature, so it's something specific in regards to the transmission cooling system.
At this point it doesn't matter if it's an LS1, LS6, LS7, or LS whatever. The problem is in the trans, the tune, and/or the trans cooling. If a stall converter has been installed, depending on how high the stall is, it can generate a lot of heat quickly. In the cool ambient temps the OP was experiencing it shouldn't be that hot. To the OP: What kind of drives are you taking the car on? If you're on a highway with few stops, and the converter is locking up in OD, IMHO, there's a problem with improper cooling going on. I have a 3,200 stall Yank converter. 20 years/almost 100,000 miles on it. My trans has a small B&M 70264 cooler added to whatever the radiator cooler can do. The only time I ever get to 200°+ is a lot of stop and go driving at 2 minute long red lights in Florida. That and going up a mountain grade in the Smoky Mountains National Park where the converter cant lock up. Even then I only see 220°, tops. If your converter still locks up without slipping, and it shifts correctly, I'd drop the pan and change the fluid and filter. If that all checks out, take the car to a competent shop and have them check the tune before you need a new trans. BTW, my 4L60E has about 150,000 miles on it, and never been apart.....Yet!!
At this point it doesn't matter if it's an LS1, LS6, LS7, or LS whatever. The problem is in the trans, the tune, and/or the trans cooling. If a stall converter has been installed, depending on how high the stall is, it can generate a lot of heat quickly. In the cool ambient temps the OP was experiencing it shouldn't be that hot. To the OP: What kind of drives are you taking the car on? If you're on a highway with few stops, and the converter is locking up in OD, IMHO, there's a problem with improper cooling going on. I have a 3,200 stall Yank converter. 20 years/almost 100,000 miles on it. My trans has a small B&M 70264 cooler added to whatever the radiator cooler can do. The only time I ever get to 200°+ is a lot of stop and go driving at 2 minute long red lights in Florida. That and going up a mountain grade in the Smoky Mountains National Park where the converter cant lock up. Even then I only see 220°, tops. If your converter still locks up without slipping, and it shifts correctly, I'd drop the pan and change the fluid and filter. If that all checks out, take the car to a competent shop and have them check the tune before you need a new trans. BTW, my 4L60E has about 150,000 miles on it, and never been apart.....Yet!!
I am in southern Missouri. Today I install a cheap trans cooler. I took it out for an hour and a half and got to 199 and could not get past that. I drove it hard and through a lot of hills. When I took it on the highway it dropped to 185. Last weekend on the highway it just kept rising. I will take it for a longer drive tomorrow.
Glad to hear that the auxiliary cooler is working, I am however curious because the radiator oil cooler should have kept the oil temperature about the same as the engine coolant.