What you have is normal for a LLY. I know, I have one. What is happening is normal for all trucks, work the engine on a hot day the fan cools things off. But the 04 & 05 LLY trucks have a cooling capacity that is only marginal, the 06 trucks have a 30% larger radiator. So the fan comes much sooner and at lower ambient temperatures. And worst of all, the fan won’t even hold the temperatures in check on a long hard pull. We bought our 05 because we wanted to buy a trailer like we now have, and knew our 6L gas 2500HD wasn't enough truck. What we got was a truck that couldn’t do the job on a 100 degree day. Like ib516 said, go to the Diesel Place and read. Then get one of these.
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We put on of these Ron Davis made auxilery radiators in our truck (the picture is not mine) and have not looked back.