Fat burns well.
Their was a few experiments done a few years ago into burning corpses, I think it related to spontaneous combustion, more importantly
how the bodies of people had reached temperatures hot enough to cause bone to be burnt away.
If memory serves correctly one of the experiments they conducted was to get a pig, stick some blankets around it, pour a small amount of ethanol onto the blankets, throw on a match and come back a few days later.
The blankets and ethanol burn slowly but at a high temperature, this causes the subcutaneous fat to liquefy and start leaking through the skin, the high temperatures of the burning blanket/clothing ignite the fat and raise the temperature of the fire. Fat takes quite a while to ignite, but once it does it burns at a high temperature and takes a lot to put out (plus it burns for a long time).
In the long run almost all of a body will be destroyed.
Alternatively look at a chip pan fire then re-think the fat doesn't burn bit