Yes, that is correct. You want to use water that is slightly warmer than body temperature (never dry heat, this will damage the tissues further)...and be prepared for a significant amount of pain as the tissues thaw. I managed to get second-degree frostbite on my fingertips a couple of years ago during an exceptionally cold winter hike (combination of factors, including pre-existing Raynaud's syndrome, different liner gloves than usual b/c my wool ones had shrunk, a really cold day, a large, slow-moving group that made a lot of stops, and me not paying enough attention) and will say that rewarming those fingers was probably the most painful thing I have experienced in my life thus far. I was using a sink full of warm water at the little restaurant where we had stopped to eat after the hike, so the only medication I had available for pain was Tylenol...and it didn't do much! Then there was the 6+ week recovery, during which time it was quite uncomfortable to do much of anything requiring hands. Moral of the story: you don't want frostbite!!

ETA: Rewarming should only be done if you are CERTAIN the area will not refreeze; if it does, there will be much more severe damage than by waiting until you are truly out of the cold.