State of the art of insulation systems for superconducting power components are based on liquid nitrogen. One disadvantage of these insulation systems is their significantly reduced dielectric strength, if gas bubbles occur due to heat losses during operation of the component. In previous research work, syntactic foam has been found to be a promising solid alternative insulation system, i.e., regarding its dielectric strength. For the design of insulation systems, the thermal conductivity is important to know as well. For this purpose, a test setup to determine the thermal conductivity of syntactic foam at cryogenic temperatures is developed. Syntactic foam consists of a polymer matrix and embedded hollow microspheres, which have diameters of several 10 $\mu\text{m}$. Compared with pure polymers syntactic foam features a lower density and a reduced thermal contraction. In this paper, epoxy resin and unsaturated polyester resin serve as matrix materials. Borosilicate glass and a ceramic are used as hollow microspheres' wall materials. Due to the investigation results, it can be observed that syntactic foam's thermal conductivity is reduced when syntactic foam is cooled from ambient temperature to liquid nitrogen temperature. Furthermore, filling the matrix materials with glass spheres leads to a decrease, whereas ceramic spheres lead to an increase of syntactic foam's thermal conductivity.