One problem related to battery has been reported for the 2007 Dodge Ram 3500. The most recently reported issues are listed below.
At 35,000 miles the engine quit. I could smell wires burning. The box that holds the fuses melted with no blown fuses. They replaced the box. After 12,000 mores miles the engine quit on the highway and the fuse box caught fire this time. I raised the hood and saw sparks jumping around and a flame in the box with a lot of smoke. I quickly disconnected the battery and put out the fire.