We present a cryogenic method for the measurement of total hemispherical emissivity and absorptivity of various materials at temperatures from 320 K down to ≈20 K. In absorptivity measurement the temperature of the examined sample is kept at ≈5 K–35 K. Radiative heat flow between two plane parallel surfaces of 40 mm in diameter disk samples placed in a vacuum, a sample and a disk with reference surface, is absorbed by a colder sample and sinks into an LHe bath via a thermal resistor (heat flow meter). Heat flow is measured by substitution method, using thermal output of an electrical heater for heat flow meter calibration. A great deal of attention is paid to the estimation of uncertainties associated with this method. Capabilities of the instrument are demonstrated by the absorptivity and emissivity measurement of the pure aluminium sample. The expanded fractional uncertainty (k = 2) in emissivity ε = 0.0041 measured at ≈30 K for pure aluminium is less than 11% and for values of emissivity ε > 0.0053 measured above 60 K the uncertainties are below 7%. The method was designed primarily for the measurement of highly reflective materials like pure metals, nevertheless high emissivity of the reference sample also enables the measurement of non-metallic materials with reasonable accuracy.