The evolution of the structure of iodine chains in iodine-doped polyacetylene has been followed as a function of temperature. It is shown that these chains exhibit a disorder of the second kind characterized by the lack of long-range order in chain direction. A low-temperature improvement of intra-chain order demonstrates that a substantial part of this disorder is thermal in nature. A parallel is drawn to similar effects frequently observed in crystalline iodine chain organic charge transfer salts. Furthermore, fresh samples with a nominal composition CHI0,24 are unstable under the X-ray beam. They exhibit a slow transition toward an apparently stable form corresponding to CHI0,19. The diffraction pattern in chain direction of this form can be quantitatively explained with a simple model using triiodide chains only. A comparison with other models proposed in the literature is made.