Two things you can do (which I can think of) to eliminate the transmission as the culprit:
When you pull the dipstick, if you smell the transmission fluid and it doesn't smell burnt (there's a DISTINCT difference when it is burnt) and is a nice cherry color as you've already stated, it should be in good shape.
On the radiator, there are two small hard lines ...
One way to break, and then need to replace, expensive components like catalytic converters and exhaust manifolds is to dump cold water on them when they are hot... The cats can run between 800 to 1000 degrees C on the inside , so even with the insulation that is fitted around them they do get very hot and they are meant to.
Prices for cats range from about $...
Both exhaust headers and catalytic converters are meant to get really hot under normal operation, well in excess of the boiling point of water.
Though I don't have the specific thermostat rating for this model, 85 °C coolant temperature strikes me as quite unremarkable; neither too hot nor too cold.