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A closed form analytical solution of the Pennes' bioheat equation was obtained for temperature distributions in the skin tissue subject to the sinusoidal heat flux. Phase shifts in the surface temperature response were revealed to be related to local blood perfusion rate and heating frequency. The influence of the thermal contact resistance on the perfusion estimation was investigated. It has been proved that this influence is relatively small because of the phase shift based estimation and can be effectively eliminated by application of highly conductive grease. This analysis provides the theoretical foundation for a new noninvasive modality of blood perfusion estimation based on the surface temperature measurement which can have significant applications in future clinical practices.