We use the thermofield dynamics (TFD) formalism to obtain the energymomentum tensor for the Kalb-Ramond (KR) field in a topologyThe compactification is carried out by a generalized TFD-Bogoliubov transformation that is used to define a renormalized energy-momentum tensor. The expressions for the Casimir energy and pressure at finite temperature are then derived. A comparative analysis with the electromagnetic case is developed, and the results may be important for applications, as in cuprate superconductivity, for instance.