  We observe the continuous emission of photons into a waveguide from a
superconducting qubit without the application of an external drive. To explain
this observation, we build a two-bath model where the qubit couples
simultaneously to a cold bath (the waveguide) and a hot bath (a secondary
environment). Our results show that the thermal-photon occupation of the hot
bath is up to 0.14 photons, 35 times larger than the cold waveguide, leading to
nonequilibrium heat transport with a power of up to 132 zW, as estimated from
the qubit emission spectrum. By adding more isolation between the sample output
and the first cold amplifier in the output line, the heat transport is strongly
suppressed. Our interpretation is that the hot bath may arise from active
two-level systems being excited by noise from the output line. We also apply a
coherent drive, and use the waveguide to measure thermodynamic work and heat,
suggesting waveguide spectroscopy is a useful means to study quantum heat
engines and refrigerators. Finally, based on the theoretical model, we propose
how a similar setup can be used as a noise spectrometer which provides a new
solution for calibrating the background noise of hybrid quantum systems.
