A cluster approach has been developed with the inclusion of the well known and traditionally employed transient plane source (TPS) technique for a comprehensive set of measurements of the thermal transport features of high- superconductors at low temperature. The present work shows the experimental arrangement containing a resistive element, `the TPS element', made of nickel material which serves the purpose of heat source and temperature sensor. From the practical point of view the main goal of the work is to design a simple cryogenic system and a sample holder configuration together for low-temperature measurements (84 - 293 K). The whole experimental arrangement is linked with the vacuum system containing a rotary pump for vacuum purposes. The apparatus is calibrated with a disc-shaped fused quartz sample for low-temperature measurements and carbon steel samples for room-temperature measurements taken as reference standard materials. Large disc-shaped superconducting samples (Y123 and Bi2223) are studied for thermal properties with the same designed apparatus. The thermal conductivity values for the samples are 2.695 and 0.944 at the transition temperature respectively. A sharp increase below in the thermal conductivity curve for both the samples is observed.