The temperature dependence of the charge-carrier mobility provides essential insight into the charge transport mechanisms in organic semiconductors. Such knowledge imparts critical understanding of the electrical properties of these materials, leading to better design of high-performance materials for consumer applications. Here, we present experimental results that suggest that the inhomogeneous strain induced in organic semiconductor layers by the mismatch between the coefficients of thermal expansion (CTE) of the consecutive device layers of field-effect transistors generates trapping states that localize charge carriers. We observe a universal scaling between the activation energy of the transistors and the interfacial thermal expansion mismatch, in which band-like transport is observed for similar CTEs, and activated transport otherwise. Our results provide evidence that a high-quality semiconductor layer is necessary, but not sufficient, to obtain efficient charge-carrier transport in devices, and underline the importance of holistic device design to achieve the intrinsic performance limits of a given organic semiconductor. We go on to show that insertion of an ultrathin CTE buffer layer mitigates this problem and can help achieve band-like transport on a wide range of substrate platforms.