For both polyacrylonitrile homopolymer and copolymers(homo- and co-PANs) prepared in dimethylsulfoxide(DHSO) solution by radical polymerization induced by azo-bis-isobutyronitrile(AIBH) , the thermal behavior studied via DSC technique was discussed in relation to the characteristics of polymers. It has been found that, for the non-isothermal stabilization of homo-PAHs under nitrogen and air atmospheres. the initiation and the maximum temperatures for the stabilization are not influenced by molecular weight and molecular weight distribution characteristics of polymers. However, under isothermal stabilization under air, longer time is required by the polymers with higher content of high molecular weight fraction. i.e. Mw>3$ imes$105. It has also been confirmed that the addition of comonomer and air atmosphere favor the stabilization of polymers by lowering the initiation temperature, slowing down the reaction rate, and extending the temperature range within which the stabilization may be completed. From the isothermal stabilization of co-PANs. it was believed that the temperature of 24$0^{circ}C$ might have practical significance.