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All surfaces are rough to some extent and therefore only a small portion of surfaces actually comes into contact when they are brought together. Therefore heat flow from one object to another is retarded by this incomplete contact, resulting in thermal contact resistance (TCR). Minimizing the TCR is important for many different applications where dissipating heat is important, such as in micro- and high-power electronics. This paper presents a simplified closed-form method for modeling TCR while considering the multiscale nature of surfaces in the contact mechanics and heat transfer theory. When modeling the contact between surfaces, it is important to consider the multiple scales of roughness that exist. Many rough surface contact models exist in the recent literature, but they can be difficult to implement and use for TCR predictions. This paper derives and presents a simplified closed-form multiscale model of TCR. The results are then compared with experimental measurements of the TCR for copper samples and with other existing models. The comparison shows relatively close agreement with the closed-form multiscale model.