The apparatus used in the measurement of the low-temperature specific heat of a metal by the temperature-wave method consists basically of a rod of the metal, one end of which is in thermal contact with a bath while at intervals along the rod are a heater and two thermometers. Two quantities are measured: the first is the velocity of propagation down the rod of temperature waves of known frequency generated by an alternating current in the heater; the second is the temperature gradient down the rod produced by a steady current in the heater. These measurements allow respectively the thermal diffusivity D and the thermal conductivity k to be derived; the ratio k/D is the specific heat of the rod per unit volume. The accuracy with which this ratio can be measured is comparable with that of the conventional static method of specific-heat measurements. The most important differences between the two methods of specific-heat measurements are that (i) the static method requires the specimen to be carefully isolated from its surroundings, while in the temperature-wave method the specimen always remains in thermal contact with them, (ii) that the temperature-wave method uses much smaller specimens than the other, and (iii) that it is hoped that it will be applicable with little loss of accuracy down to the temperatures attainable by adiabatic demagnetization. The method was tried on copper and aluminium specimens in the liquid-helium temperature range, using frequencies between 16 and 1800 c/s. The design of suitable thermometers and electronic circuits is described. Among other corrections, those due to the finite length of the specimens were investigated and are discussed in detail, and a method of detecting and eliminating differences of thermal time-lags through the thermometers is described. The method appears to give results which are free from systematic errors.