Technical superconductors for 50-Hz application, operated at liquid-helium temperature, are designed for very low ac losses. These low losses cannot be measured calorimetrically on short samples of conductors with the conventional measuring techniques, but only on coils wound of several hundreds of meters of wire. We describe here the development of a technique which allows the measurement of ac losses with a resolution of 10-8 W. The method is similar to a thermal conductivity measurement. The sample is placed into a vacuum vessel and connected via a thermal resistance to the liquid-helium bath. Losses in an alternating magnetic field lead to a temperature increase which is a measure of the dissipated power. Calibration is done with an ohmic heater connected to the sample.