Hyporheic and groundwater fluxes typically occur together in permeable sediments beneath flowing stream water. However, streambed water fluxes quantified using the thermal method are usually interpreted as representing either groundwater or hyporheic fluxes. Our purpose was to improve understanding of co-occurring groundwater and hyporheic fluxes using streambed temperature measurements and analysis of one-dimensional heat transport in shallow streambeds. First, we examined how changes in hyporheic and groundwater fluxes affect their relative magnitudes by reevaluating previously published simulations. These indicated that flux magnitudes are largely independent until a threshold is crossed, past which hyporheic fluxes are diminished by much larger (1000-fold) groundwater fluxes. We tested accurate quantification of co-occurring fluxes using one-dimensional approaches that are appropriate for analyzing streambed temperature data collected at field sites. The thermal analytical method, which uses an analytical solution to the one-dimensional heat transport equation, was used to analyze results from a numerical heat transport model, in which hyporheic flow was represented as increased thermal dispersion at shallow depths. We found that co-occurring groundwater and hyporheic fluxes can be quantified in streambeds, although not always accurately. For example, using a temperature time series collected in a sandy streambed, we found that hyporheic and groundwater flow could both be detected when thermal dispersion due to hyporheic flow was significant compared to thermal conduction. We provide guidance for when thermal data can be used to quantify both hyporheic and groundwater fluxes, and we show that neglecting thermal dispersion may affect accuracy and interpretation of estimated streambed water fluxes.