Most of the people murdered in the extermination camps, and then burned, were not "concentration camp inmates". They were arrested, held for only a few days at most, put on a train to the camp, where they were unloaded and gassed within a few hours. They would be hungry and a bit dehydrated from the train journey (they were not given food or water) but they still had normal levels of fat for a healthy person in the 1940s.

Its not just the fat that provided heat, protein does too. Almost everything aside from water and bone will generate heat on combustion in the human body. The average human body contains 125000 calories, which is almost double what you need to completely boil 30 kg of water. With just a bit of fuel needed to to prime the pump, so to speak, the process is completely self-sustaining. One normal healthy body contains enough fuel energy to completely burn itself to ash, plus enough left over to ignite one or two more bodies. Even emaciated bodies contain enough fuel to burn themselves to ash, and they're easier to ignite because they don't have as much water.

Human corpses are hard to ignite, but once you manage it, they burn like the blazes.