A mechanism of the high temperature ferromagnetism in polymerized fullerenes is suggested. It is assumed that some of the C60 molecules in the crystal become magnetically active due to spin and charge transfer from the paramagnetic impurities (atoms or groups), such as hydrogen, fluorine, hydroxyl group OH, amino group NH2, or methyl group CH3, dispersed in the fullerene matrix. The exchange interaction between the spins localized on the magnetically active fullerenes is evaluated using ab initio calculations. The nearest neighbour and next nearest neighbour exchange interaction is found to be in the range 0.1 ÷ 0.3 eV, that is, high enough to account for the room temperature ferromagnetism.