Why carbon no react with oxygen by exposure to heat ?

In low temperature there is no enough energy to eliminate oxygen and rather eliminate carbondioxide at the unstable side. When temperature is elevated oxygen becomes unstable and is eliminated. I think graphite is more stable than the oxygenated form naturally.

Carbon is more stable than oxygen therefore carbon can not react with oxygen

What the condition do you propose for segregation (t, P etc.)?

For some detail I refer to Korean Patent 10-2011-0135234. And I submitted a paper giving the evidendces and explanation to Chemical Engineering Communications, Manuscript ID GCEC-2012-0046

Oxygen ls larger than carbon so graphite or diamond is more stable than oxygenated form unlike silicon that can exist in stable quartz in which case silicon is larger than oxygen and silicon crystal is less stable than quartz