When heat transfers through electromagnetic waves nearby objects can catch alight if enough radiated heat reaches the object.
Conduction
In conduction a fire will spread through heat transfer, if there is a flammable material in contact with the object that absorbed the heat it can come alight.
Convection
Since cold air is heavier than hot air, hot gases and smoke rise above cold air. This hot air gets trapped in ceilings preventing it from moving higher, this then causes everything to build up. This is dangerous if breathed in and can also cause a fire to spread.