Variations in temperature within the Earth are of great interest because they indicate the thickness and, consequently, mechanical strength of the lithosphere and density variations and convection patterns in the sublithospheric mantle. Seismic tomography maps seismic velocity variations in the mantle, which strongly depend on temperature. Temperatures are, thus, often inferred from tomography. Tomographic models, however, are nonunique solutions of inverse problems, regularized to ensure model smoothness or small model norm, not plausible temperature distributions. For example, lithospheric geotherms computed from seismic velocity models typically display unrealistic oscillations, with improbable temperature decreases with depth within shallow mantle lithosphere. The errors due to the intermediate‐model nonuniqueness are avoided if seismic data are inverted directly for temperature. The recently developed thermodynamic inversion methods use computational petrology and thermodynamic databases to jointly invert seismic and other data for temperature and composition. Because seismic velocity sensitivity to composition is much weaker than to temperature, we can invert seismic data primarily for temperature, with reasonable assumptions on composition and other relevant properties and with additional inversion parameters such as anisotropy. Here, we illustrate thus‐defined seismic thermography with thermal imaging of the lithosphere and asthenosphere using surface waves. We show that the accuracy of the models depends critically on the accuracy of the extraction of structural information from the seismic data. Random errors have little effect but correlated errors of even a small portion of 1% can affect the models strongly. We invert data with different noise characteristics and test a simple method to estimate phase velocity errors. Seismic thermography builds on the techniques of seismic tomography and relies on computational petrology, but it is emerging as a field with its scope of goals, technical challenges, and methods. It produces increasingly accurate models of the Earth, with important inferences on its dynamics and evolution.