The thermoelastic effects of a traveling wave of temperature on the surface of an infinite homogeneous elastic half space are examined. The horizontal and shear strain and the tilt are principally caused by tractions in the thermal boundary layer, and they decay vertically with the scale of the horizontal wavelength of the applied temperature wave. The vertical strain is larger at the surface by the ratio of this wavelength to the thermal boundary thickness, but below the boundary layer it behaves like the other components. The burial of instruments at practical depths is unlikely to reduce significantly the thermoelastic effects except on the vertical strain.