The Law of Thermodynamics loathes to be broken by so simple a means.
In other words, his corporeal components will eventually burn themselves out without a greater influx to sustain them. We see this in the game itself, where the inner furnace fire begins to burn hotter and hotter. He does eventually just burn himself out and fall over dead. Presumably, outside magic becomes necessary resurrect him.
Mordekaiser, the nearest analog to 'indestructible', still has an Achilles's Heel. If his bones are ever destroyed, the ritual binding him to existence will break, and he will cease to exist.