Sketch of the Cenco thermal conductivity apparatus, showing copper heat receiver R and slab of insulator specimen S.
A thin slab of an insulating material, such as porcelain, wood, or styrofoam, is placed between a vessel of boiling water and a metal heat sink. Thermocouples and a Fluke 52 digital thermometer are used to measure the temperature of the slab as it heats up. From your data, the conductivity of the material (or alternatively the R-value) can be found.
Diagram adapted from Overbeck, et. al., Selective Experiments in Physics: Thermal Conductivity (Advanced Theory). Copyright 1959, Central Scientific Company.