I get asked this from time to time.
For most materials we cannot see below the surface at all, never mind measure a temperature below the surface. The vast majority of common materials are thermally opaque, this means that the camera can only detect radiation emitted from the surface. For this reason we cannot normally see below the surface, or measure below the surface. Thermography generally only includes surface temperatures, and images of surface emitted radiation.
Some materials are not thermally opaque, in this case we can see through them quite well, but these materials are not very common, and measuring temperature below the surface from a material like these (that are highly transmissive) is near impossible with thermography.