Possible equilibrium states of multilayered carbon nanoribbons are found using the chain model moving on a plane previously proposed by the authors. For very short nanoribbons only flat multilayered structures are possible, while for sufficiently long nanoribbons the lowes energy have nanoscrolls with folded structures having intermediate value of energy. Dependencies of the internal and external radii of the scrolls, as well as the number of coils on the nanoribbon length are calculated. It is found that the radial thermal espansion coefficient of nanoscrolls is two or even three orders of magnitude larger than the linear thermal expansion coefficient of diamond. Thus, carbon nanoscrolls can be used to make very sensitive temperature sensors.