Thermal dissipation at the active region of electronic devices is a fundamental process of considerable importance(1-3). Inadequate heat dissipation can lead to prohibitively large temperature rises that degrade performance(4-7), and intensive efforts are under way to mitigate this self-heating(8-12). At room temperature, thermal resistance is due to scattering, often by defects and interfaces in the active region, that impedes the transport of phonons. Here, we demonstrate that heat dissipation in widely used cryogenic electronic devices(13-16) instead occurs by phonon black-body radiation with the complete absence of scattering, leading to large self-heating at cryogenic temperatures and setting a key limit on the noise floor. Our result has important implications for the many fields that require ultralow-noise electronic devices.