Process-based models of fluid flow and heat transport in fluvial systems can be used to quantify 17 unknown spatial and temporal patterns of hydrologic fluxes and to predict system response to 18 change. In this study, a deterministic stream heat budget model, the HFLUX Stream 19 Temperature Solver (HFLUX), is developed and evaluated using field studies. Field studies are 20 conducted across two sites with different streamflow rates (0.07 vs 1.4 m 3 /s), and point sources 21 versus diffuse sources of groundwater discharge, to demonstrate model transferability. A winter 22 versus summer comparison at one site suggests latent heat flux should be derived using energy-23 based methods in summer and mass balance approaches during winter. For each field study, 24 HFLUX successfully modeled stream temperatures through space and time with normalized root 25 mean square errors of 3.0 to 6.2%. Model calibration to observed temperature data in order to 26 quantify groundwater contributions and a sensitivity analysis are demonstrated using HFLUX. 27

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Although stream temperature energy balance models are useful to predict temperature through time and space, a major unresolved question is whether fluctuations in stream discharge reduce model accuracy when not exactly represented. However, high‐frequency (e.g., subdaily) discharge observations are often unavailable for such simulations, and therefore, diurnal streamflow fluctuations are not typically represented in energy balance models. These fluctuations are common due to evapotranspiration, snow pack or glacial melt, tidal influences within estuaries, and regulated river flows. In this work, we show when to account for diurnally fluctuating streamflow. To investigate how diurnal streamflow fluctuations affect predicted stream temperatures, we used a deterministic stream temperature model to simulate stream temperature along a reach in the Quilcayhuanca Valley, Peru, where discharge varies diurnally due to glacial melt. Diurnally fluctuating streamflow was varied alongside groundwater contributions via a series of computational experiments to assess how uncertainty in reach hydrology may impact simulated stream temperature. Results indicated that stream temperatures were more sensitive to the rate of groundwater inflow to the reach compared with the timing and amplitude of diurnal fluctuations in streamflow. Although incorporating observed diurnal fluctuations in discharge resulted in a small improvement in model RMSE, we also assessed other diurnal discharge signals and found that high amplitude signals were more influential on modelled stream temperatures when the discharge peaked at specific times. Results also showed that regardless of the diurnal discharge signal, the estimated groundwater flux to the reach only varied from 1.7% to 11.7% of the upstream discharge. However, diurnal discharge fluctuations likely have a stronger influence over longer reaches and in streams where the daily range in discharge is larger, indicating that diurnal fluctuations in stream discharge should be considered in certain settings.