We investigate the effects of nanosized contact spots on the thermal contact resistance (TCR) in multiscale contacts. As the contact size decreases below the phonon mean free path, the thermal conductivity varies with the size of the contact and is not the same as its bulk counterpart. We take this into account in our model and we calculate the TCR of silicon contacted with other silicon. The TCR increases as the number of nanosized contact spots increases. However, if we do not consider the thermal conductivity reduction as the contact size decreases below the size of the phonon mean free path, there is a finite limit of the TCR. A parametric study on the effects of distance and size of the contact spots is also presented.