Since the discovery a century ago1-3 of electronic thermal noise and shot noise, these forms of fundamental noise have had an enormous impact on science and technology research and applications. They can be used to probe quantum effects and thermodynamic quantities4-11, but they are also regarded as undesirable in electronic devices because they obscure the target signal. Electronic thermal noise is generated at equilibrium at finite (non-zero) temperature, whereas electronic shot noise is a non-equilibrium current noise that is generated by partial transmission and reflection (partition) of the incoming electrons8. Until now, shot noise has been stimulated by a voltage, either applied directly8 or activated by radiation12,13. Here we report measurements of a fundamental electronic noise that is generated by temperature differences across nanoscale conductors, which we term 'delta-T noise'. We experimentally demonstrate this noise in atomic and molecular junctions, and analyse it theoretically using the Landauer formalism8,14. Our findings show that delta-T noise is distinct from thermal noise and voltage-activated shot noise8. Like thermal noise, it has a purely thermal origin, but delta-T noise is generated only out of equilibrium. Delta-T noise and standard shot noise have the same partition origin, but are activated by different stimuli. We infer that delta-T noise in combination with thermal noise can be used to detect temperature differences across nanoscale conductors without the need to fabricate sophisticated local probes. Thus it can greatly facilitate the study of heat transport at the nanoscale. In the context of modern electronics, temperature differences are often generated unintentionally across electronic components. Taking into account the contribution of delta-T noise in these cases is likely to be essential for the design of efficient nanoscale electronics at the quantum limit.