Carbon nanotubes (CNTs) may be useful due to their sound thermo-mechanical properties. The present work deals with the evaluation and analysis of elastic properties and coefficient of thermal expansions (CTEs) of a CNTs-based 2D plane woven fabric composite material system where the CNTs are radially grown on the surface of the carbon fiber. Detailed constructional features of the proposed trans-scale composite material system is explained in detail. The mathematical modeling for the material properties of each constituent or building block of the hybrid composite is developed. The mathematical model for the thermo-elastic properties of yarns is also formulated based on strength of material method whereas the thermo-elastic properties of representative unit cell is based on the unit cell method. Various numerical results have been obtained by varying the CNTs content, carbon fiber contents, and temperatures. Effects of different geometrical parameters (such as yarn thickness, yarn width, and the ratio of gap length to yarn width of the yarn) on the elastic properties as well as the CTEs are also investigated. © 2017 Taylor & Francis Group, LLC.