  A mechanism of the high temperature ferromagnetism in polymerized fullerenes
is suggested. It is assumed that some of the C$_{60}$ 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 NH$_2$, or methyl group CH$_3$, dispersed in the
fullerene matrix. The exchange interaction between the spins localized on the
magnetically active fullerenes is evaluated using \textit{ab initio}
calculations. The nearest neighbour and next nearest neighbour exchange
interaction is found to be in the range $0.1\div 0.3 $ eV, that is, high enough
to account for the room temperature ferromagnetism.
