What happens depends whether it is being heated in the presence or absence of oxygen. For example, in the manufacture of coke (mostly carbon), coal is heated without oxygen and from Coke Production For Blast Furnace Ironmaking:
The coal-to-coke transformation takes place as follows: The heat is transferred from the heated brick walls into the coal charge. From about 375°C to 475°C, the coal decomposes to form plastic layers near each wall. At about 475°C to 600°C, there is a marked evolution of tar, and aromatic hydrocarbon compounds, followed by resolidification of the plastic mass into semi-coke. At 600°C to 1100°C, the coke stabilization phase begins.
Without oxygen, the carbon will remain upto its boiling point of 3825 °C.
With oxygen, carbon as coke with start combustion at its autoignition temperature of about 700°C