The ability to control and measure the photonic occupation of propagating microwave modes down to very low temperatures is indispensable for quantum information processing with superconducting circuits, and may open opportunities for studies of thermodynamics at the nanoscale. Yet, the methods used so far are indirect, require sophisticated time-resolved measurements, and have poor temporal resolution. Here we propose and experimentally demonstrate primary thermometry of propagating microwave modes, using a transmon-type superconducting circuit. We measure the radiation temperature of a highly attenuated coaxial cable connecting room-temperature electronics to the base plate of a dilution cryostat, in the range of 200 mK down to 35 mK and with resolution well below one per mil in thermal occupation. To increase the radiation temperature in a controlled fashion, we either inject calibrated, wideband digital noise, or heat the device and its environment. In the latter case, we observe the thermalization dynamics of the microwave modes in real time. Our technique can be used to benchmark filtering and attenuation schemes for superconducting quantum information processors; at the same time, it provides a novel tool for experiments in quantum thermodynamics.