In general, double-based powders do burn a little hotter than single-based powders, but exactly how much warmer depends on the amount of nitroglycerin. One Australian military report (the most detailed I've found on barrel erosion) points out that the nitrogen in nitroglycerin actually hardens the surface of barrel steel a little, counterbalancing the effect of higher temperatures.
Apparently the big factor in bore erosion isn't the exact temperature of the powder burn, but the amount of powder and the duration of the burn. This is why large powder charges for the bore-size fry barrels quicker, and also probably why shooters using some of the newer ultra-progressive-burning powders report quicker bore erosion.
