Hollow conductors have been widely employed in many electrical devices such as electrical machines, transformers, induction heaters and in fast ramping magnets in order to facilitate the flow of electrical current while enabling efficient thermal cooling [Mol+24]. Simulation wise, hollow conductors are very challenging to compute as they impose a multi scale problem, both geometrically and physically. The goal of this work is to develop an efficient homogenization technique for the thermal simulation of a single hollow conductor. The resulting surrogate model shall be embedded in a so-called unit-cell method, where every hollow conductor in a device is modeled as a homogenized cell, leading to an efficient numerical method for the simulation of hollow conductor coils