In this work, the size effect on the effective through-thickness conductivity of heterogeneous plates is expressed in second-order Hashin-Shtrikhman bounds and a third-order correlation approximation is studied. By taking into account the homogeneous temperature boundary conditions, the exact Green operator for the plate is first established. Then , the respective bounds and correlation approximation are constructed. With the help of the methods based on the Fast Fourier Transform (FFT), the bounds and correlation approximation for the effective through-thickness conductivity are computed for the plates reinforced or weakened randomly either by spherical particles or unidirectional fibers. The numerical results show that the size effect on the effective through-thickness conductivity is more significant than the one of the effective in-plane conductivity.