I think RoyBrady is correct---your converter is likely boiling off your batteries. If you get a multi-meter, I would bet you have a shorted cell or two. When the water boils off the battery, sulfides form on the exposed lead and eventually grow to touch a neighboring cell. Once that happens, the cells become electrically one cell. If I recall correctly, common 12 volt batteries have 6 cells that produce a little over 2 volts each. When a cell is bridged with another cell, the battery will only produce 10 volts or so because the cells become one. I suspect that since 12 volt appliances (lights, etc.) were meant to draw 12 volts and only 10 volts are available, more amperage is drawn to compensate. More amperage means more resistance in wire meant for 12 volts, which means more heat.
Of course, all of this is a guess....