Two common refrains about using the one‐dimensional advection diffusion equation to estimate fluid fluxes and thermal conductivity from temperature time series in streambeds are that the solution assumes that (1) the surface boundary condition is a sine wave or nearly so, and (2) there is no gradient in mean temperature with depth. Although the mathematical posing of the problem in the original solution to the problem might lead one to believe these constraints exist, the perception that they are a source of error is a fallacy. Here we develop a mathematical proof demonstrating the equivalence of the solution as developed based on an arbitrary (Fourier integral) surface temperature forcing when evaluated at a single given frequency versus that derived considering a single frequency from the beginning. The implication is that any single frequency can be used in the frequency‐domain solutions to estimate thermal diffusivity and 1‐D fluid flux in streambeds, even if the forcing has multiple frequencies. This means that diurnal variations with asymmetric shapes or gradients in the mean temperature with depth are not actually assumptions, and deviations from them should not cause errors in estimates. Given this clarification, we further explore the potential for using information at multiple frequencies to augment the information derived from time series of temperature.

Streambed erosion and deposition are fundamental geomorphic processes in riverbeds, and monitoring their evolution is important for ecological system management and in‐stream infrastructure stability. Previous research showed proof of concept that analysis of paired temperature signals of stream and pore waters can simultaneously provide monitoring scour and deposition, stream sediment thermal regime, and seepage velocity information. However, it did not address challenges often associated with natural systems, including nonideal temperature variations (low‐amplitude, nonsinusoidal signal, and vertical thermal gradients) and natural flooding conditions on monitoring scour and deposition processes over time. Here we addressed this knowledge gap by testing the proposed thermal scour‐deposition chain (TSDC) methodology, with laboratory experiments to test the impact of nonideal temperature signals under a range of seepage velocities and with a field application during a pulse flood. Both analyses showed excellent match between surveyed and temperature‐derived bed elevation changes even under very low temperature signal amplitudes (less than 1°C), nonideal signal shape (sawtooth shape), and strong and changing vertical thermal gradients (4°C/m). Root‐mean‐square errors on predicting the change in streambed elevations were comparable with the median grain size of the streambed sediment. Future research should focus on improved techniques for temperature signal phase and amplitude extractions, as well as TSDC applications over long periods spanning entire hydrographs.