Parabolic heat conduction models are considered. The validity of using a microscopic under harmonic fluctuating boundary heating source is investigated. It is found that using the microscopic parabolic heat conduction model is essential when ω ̄ C l /G>0.1 . The phase-shift between the electron gas and solid lattice temperatures is found to be tan −1( ω ̄ C l /G) . This phase-shift reaches a fixed value of 1.5708 rad at very large values of ω ̄ C l /G . It is found that using the microscopic parabolic heat conduction model is essential when ω ̄ >1×10 9 rad/s for most metallic layers regardless of their thickness.