An innovative cooling strategy for the mirrors of the transmission line of the electron cyclotron heating (ECH) of a fusion research reactor, the divertor tokamak test (DTT) facility, is presented and investigated here based on triply periodic minimal surfaces (TPMSs). After the check on the manufacturability of gyroid and Split-P lattices of unit cell size ranging from 3 to 8 mm, extensive numerical investigations by conjugate heat transfer analyses have been performed. The heat removal capability has been assessed together with the pressure drop for all heat sinks. The temperature field in the mirror has been evaluated and used for the assessment of the deformation of the mirror reflective surface. The results show that all tested TPMSs are highly efficient in the heat removal, with low hotspot temperatures, minimal pressure drop, and low deformation of the reflective surface.