In polycrystalline non-cubic materials temperature variations can cause internal thermoelastic microstresses due to the anisotropy of the thermal expansion coefficient in individual grains. These stresses were called [1] microstructural thermal anisotropy stresses (MTAS). If the MTAS exceed the critical stress at which slip (or twinning) starts in any of the crystallographic systems of plastic shear in an individual grain, this grain experiences plastic deformation. This really occurs on heating, cooling and thermocycling of soft polycrystalline metals. The phenomenon was first detected by Boas and Honeycombe in the 1944-47ies [2], who tried to estimate roughly the order of MTAS magnitude. V.A. Likhatchev obtained formulae for the order of magnitude calculation of MTAS in polycrystals of all non-cubic symmetries. He used the model of an elastically and thermally anisotropic grain immersed into isotropic medium [1]. We employ Likhatchev's model to calculate the MTAS in the grains of coarse- and ultrafine grain (nanostructured) titanium on cooling below room temperature. The MTAS effect on the mechanical behavior of titanium is estimated.