With the application to engineering practice, the study of the scattering of thermal waves using innovative and comprehensive methods is becoming increasingly important. The thermal wave scattering by an elliptic subsurface hole in a block with two boundaries is discussed based on the non-Fourier heat conduction equation, employing the complex function method and the conformal mapping method, and a general solution for the thermal wave scattering is given. The numerical results of temperature distributions around a subsurface hole are presented and the effects of geometrical and physical parameters on the temperature distributions were analyzed. The wave number, the shape and position of the hole, the scale of the block, and the frequency of the heat load were found to have great effects on distributions and variations of temperature. The findings of this study could be helpful in providing better understandings of infrared thermal wave imaging, the physical inverse problem, and the evaluation of internal holes in materials.