Thermal conductivity of an electron gas with non-standard dispersion relations is studied by using the Fermi-Dirac statistics. To that end, a cubic transmission line to model a left-handed system and its corresponding right-handed system is used. The heat capacity and the group velocity for both systems are obtained and studied, allowing to discern the behavior of thermal conductivity in the high and low temperature limits. Analytical expressions for these limits are obtained and a numerical analysis that supports the results is performed. (C) 2018 Elsevier B.V. All rights reserved.