Thermoelastic logging can detect differences between the borehole fluid and the far-field formation temperatures. Radial temperature distributions caused by such temperature differences introduce thermal stresses in the near-wellbore region that perturb the borehole Stoneley and flexural dispersions. Thermal stresses are determined in terms of the rock Lame constants (λ and μ) and thermal expansion coefficient (α) for a given radial variation of temperature between the borehole fluid and far-field formation temperatures. This paper describes a volume integral formulation that computes changes in the borehole dispersions caused by the presence of radially varying thermal stresses away from the borehole surface. Differences between borehole dispersions in the presence and absence of such thermal deformation can be used to estimate the rock thermoelastic constant and associated thermal expansion coefficient. These properties are estimated within the radial depth of investigation of sonic tools when the borehole fluid temperature and radial variation of rock temperature away from the borehole surface are known. Characteristic differences in the dipole and Stoneley dispersions provide evidence of either increasing or decreasing temperatures away from the borehole surface. These signatures can be used to estimate the magnitude of tensile or compressive thermal stresses at the borehole surface together with the radial boundary of the temperature variation until the steady-state far-field temperature is attained. Differences between the borehole fluid and steady-state formation temperatures can, therefore, be used to introduce tensile fractures at the borehole surface or to maintain wellbore stability by maintaining thermal stresses within a safe window.