Dodge auto trans with cummins engine?

It's doable. Most guys who do that swap use the 2000 series transmission from school buses, delivery trucks, and so forth. The swap is expensive, time consuming, and has to be done by an experienced and well qualified shop. The most difficult aspect is integrating the electronics, especially on that generation of engine and vehicle. Vehicle speed sensors, emissions control, and engine management all take inputs from the transmission, which will have to be created or compensated for in order to maintain road worthiness. Realistically, you're much better off on a cost-basis to either sell the truck and buy the Duramax in a GM vehicle, or, if you're having transmission durability issues with the Cummins, sell the truck and buy a manual transmissioned vehicle. If you are not having durability issues and are not towing very heavy (14,000lbs plus) loads, don't worry about it, and drive your truck into the ground around the motor, which will last you 400,000 miles with relative ease. Put a transmission cooler on the vehicle, a transmission fluid temperature gauge on it, and just drive easy. Remember, your truck and its powertrain were designed to operate within the parameters of the owners manual. If you regularly tow so much that you're burning up transmissions, then either you aren't maintaining it properly, driving incorrectly, or are overloaded, and need to move up to something like a medium duty truck.

Won't hurt to check the tranny out, it could be burning up and binding, that would explain high rpm's and high temperture. Check fluid and see if it is still nice and red, if it is brown and burnt smelling take it to transmission shop and have it checked, maybe you will get lucky and a simple band adjustment will fix it. I don't know much about the Cummings so I could be wrong on this and it might be an engine problem too but still I won't hurt to check the tranny. Good luck!