Positron-lifetime measurements have been made in undoped and polymers 0.8 wt %-iodine-doped polyacrylonitrile (PAN) under annealing from room temperature to 160-degrees-C. From the measured lifetimes, the free-volume size is calculated following the treatment of Nakanishi, Jean, and collaborators. The variation in free-volume size as function of temperature seems to suggest molecular-chain-folding processes in amorphous regions of the polymer, positron trapping at kink-type defects, and at the interface between crystalline and amorphous regions at lower temperatures. This study indicates that in the undoped state, the polymer has a glass transition temperature at 90-degrees-C which is shifted toward lower temperature in the doped state by 30-degrees-C. The results also suggest the degradation of the polymer in the two states after 100-degrees-C and the effect of annealing is only on the size but not on the density of free-volume sites.