Thin epitaxial films have a great potential to be used in real life applications, such as oxide-on-silicon. However, they often contain a large amount of defects, leading to an enhanced electrical conductivity. This could be desirable in some applications (i. e. memristors), but the mechanism is not fully understood. Here we report on the investigation of epitaxial barium strontium titanate thin films deposited on strontium titanate single crystal substrates (Ba0.7Sr0.3TiO3/SrRuO3//SrTiO3 heterostructures) with a controlled epitaxial strain. The impedance analysis allowed us to propose a model, which explains changes in the temperature dependence of the conductivity based on the strain-dependent anisotropic change of electron/hole mobility.