The highly aromatic structure of the macromolecular organic matter (OM) of the Murchison and Orgueil meteorites was recently shown to contain free organic radicals which are concentrated in micro-regions in contrast with terrestrial samples which always show an homogeneous distribution of radicals. An additional signature is revealed, in the present study, by the evolution of the radical concentration with temperature. Whereas in terrestrial samples, this concentration is independent of temperature (Curie magnetism), a significant increase is observed above 150 K in the two meteorites. Based on the electronic structure of organic radicals, calculated by Extended Hückel and Density Functional methods, this behavior was assigned to the occurrence of diradicaloid moieties hosted by aromatic structures of 10 to 15 rings and having a quinoidal structure. They represent 40 and 25% of the total radicals in Orgueil and Murchison, respectively. The search for the cosmochemical interpretation of this unique observation should open a new field of experimental investigations.