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The recent increase in distributed power generation is highlighting the demand to investigate and implement better and more efficient power distribution grids. High-temperature superconducting (HTS) DC transmission cables have the potential to address the need for more efficient transmission and their usage is expected to increase in the future. Thermal modeling of HTS DC cables is a critical tool to have in order to better understand and characterize the operation of such transmission lines. This paper introduces a general computational model for a HTS DC cable. A physical model, based on fundamental correlations and principles of classical thermodynamics, mass and heat transfer, was developed and the resulting differential equations were discretized in space. Therefore, the combination of the physical model with the finite volume scheme for the discretization of the differential equations is referenced as Volume Element Model, (VEM). The model accounts for heat transfer by conduction, convection and radiation obtaining numerically the temperature distribution of superconductive cables operating under different environmental, operational and design conditions. As a result, the model is expected to be a useful tool for simulation, design, and optimization of HTS DC transmission cables.