2003 Hyundai Sonata Car overheats in stop&go traffic &a

We replaced the engine in my car with a used 2005 Sonata engine. We were told by the dealership it was the same engine and not a problem. After my husband and my brother put the 2005 engine into the car, it's been running warm in stop and go traffic and with actually go into the red when I'm pulling a very steep grade. I drive through mountains everyday to work and it doesn't do it all the time, just when I'm really pushing the engine, like if I have to pass someone on a grade. We've replaced the thermostat, had the radiator checked, and had the fans checked. There was an issue with the fans but they were fixed and the problem disappeared for a while and then came back. The mechanic insists that the fans are working properly now and that isn't the problem. We've replaced the temperature sensor in the engine as well. Nothing has worked and we were told by the dealership that it is an imcompatability between the 2005 engine and the 2003 computer. Any thoughts on this?