Heat-pulse tracers are a promising field method to measure Darcy flux in the hyporheic zone. Interpretation of data collected from such tests typically assumes knowledge of the direction of local Darcy flux (vertical) and relies on simplified heat transport models with one-dimensional fluid flow and heat transfer. These assumptions are seldom valid due to complex flow geometry, heterogeneity, and the presence of localized heat sources. We derive a set of analytical expressions that obviate the need for these simplifying assumptions, thus substantially improving the capabilities of existing field instruments without requiring additional measurements. These closed-form solutions account for tensorial nature of heat-transfer parameters, and are obtained by using Green's functions and rotational coordinate transformations. The approach simplifies data collection, estimates three-dimensional Darcy flux, relates fluid flow to heat transfer properties of the host medium, and can facilitate inverse modeling. Field applications of our solutions and their ramifications for data collection and analysis are discussed.