Heat-as-a-tracer has become a common method to quantify surface water-groundwater interactions (SW/GW). However, the method relies on a number of assumptions that are likely violated in natural systems. Numerical studies have explored the effects of violating these fundamental assumptions to various degrees, such as heterogeneous streambed properties, two-dimensional groundwater flow fields and uncertainty in thermal parameters for the 1-dimensional heat-as-a-tracer method. No work to date has addressed the impacts of non-uniform, three-dimensional groundwater flows on the use of heat-as-a-tracer to quantify SW/GW interactions. Synthetic temperature time series were generated using COMSOL Multiphysics for a three-dimensional cube designed to represent a laboratory setup of homogeneous, isotropic sand with a sinusoidal temperature variation applied to the top. We compare temperature-derived fluxes to model-generated fluxes to assess the performance of methods using temperature to quantify 1D vertical fluxes in response to multi-dimensional groundwater flows. Both increasingly non-uniform and non-vertical groundwater flow fields result in increasing errors for both amplitude-ratio-derived groundwater flux and temperature-derived effective thermal diffusivity. For losing flow geometries, errors in temperature-derived effective thermal diffusivity are highly correlated with errors in temperature-derived flux and can be used to identify if underlying assumptions necessary for heat-as-a-tracer for quantifying groundwater flows have been violated. For this model set-up, when groundwater flows are non-uniform, the thermal method generally calculates fluxes outside the range occurring between temperature sensor pairs. When errors are low (15% of flux calculations), temperature derived fluxes more closely match the minimum magnitude flow occurring between the sensors.