A measurement system has been designed and built for the specific application of measuring the effective thermal conductivity of a composite, nuclear-fuel compact (small cylinder) over a temperature range of 100 °C to 800 °C. Because of the composite nature of the sample as well as the need to measure samples pre- and post-irradiation, measurement must be performed on the whole compact non-destructively. No existing measurement system is capable of obtaining its thermal conductivity in a non-destructive manner. The designed apparatus is an adaptation of the guarded-comparative-longitudinal heat flow technique. The system uniquely demonstrates the use of a radiative heat sink to provide cooling which greatly simplifies the design and setup of such high-temperature systems. The design was aimed to measure thermal-conductivity values covering the expected range of effective thermal conductivity of the composite nuclear fuel from 10 W . m-1 . K-1 to 70 W . m-1 . K-1. Several materials having thermal conductivities covering this expected range have been measured for system validation, and results are presented. A comparison of the results has been made to data from existing literature. Additionally, an uncertainty analysis is presented finding an overall uncertainty in sample thermal conductivity to be 6 %, matching well with the results of the validation samples.