Recycling of wood building waste has been required and wood boards are prospective recycled materials. The concept of FGM was introduced to the wood board as a base material of a floor heating system to develop an FGM board with higher energy efficiency. Two-dimensional unsteady heat transfer problem in an FGM plate with material properties of wood was analyzed, which modeled the state that the base material was heated partially. The Laplace transform and the perturbation method were applied for the analysis. The tactile warmth of a facing plate in the floor heating system, which touches to human sole directly, was discussed to avoid losing the goodness of wood.