We develop a quantitative thermodynamic model to understand the role of thermal stresses on the dielectric permittivity and tunability of (001)-textured polycrystalline monodomain strontium titanate (SrTiO3) films. This methodology is used to compute the dielectric constant and tunability of SrTiO3 films on Si, c-sapphire, LaAlO3, and MgO substrates. Results show that dielectric properties of SrTiO3 depend strongly on the growth/processing temperature TG. For substrates such as MgO that induce compressive in-plane thermal stresses, the dielectric response of SrTiO3 is enhanced. However, for SrTiO3 films on IC-compatible substrates (Si and c-sapphire), thermal stresses can significantly degrade the dielectric permittivity and tunability.