Conformational properties of polyesters based on terephthalate and cyclohexylene dicarboxylate with 1,4-cyclohexanedimethanol and 2,2,4,4-tetramethyl-1,3-cylcobutanediol are studied using RIS Metropolis Monte-Carlo simulations. The polyester single chains investigated have two different configurations, one with an all trans linkage of 1,4-cyclohexanedimethanol and 2,2,4,4-tetramethyl-1,3-cylcobutanediol, and the other in which both trans and cis linkages of these rings in the diol units were present. Incorporation of cis isomers results in a decrease in the chain dimensions, and reduces the influence of the repeat unit chemical structure on the overall conformationally averaged chain dimensions. The trend in the variation in chain dimensions with increase in temperature is found to be dependent on the structure of the polyester along with the isomer constitution of the chains. In the all-trans isomer chains, the polyester containing cyclobutylene groups were much more rigid than those with cyclohexylene groups in the backbone, as evident from the characteristic ratios and the persistence lengths. The effect of temperature, isomer linkage, nature of the aliphatic ring in the backbone and its content, on the overall chain dimensions and the persistence length, is brought out by this study.