In order to manage surface water (SW) and groundwater (GW) as a single resource, it is necessary that the interactions between them are understood and quantified. Heat, as a natural tracer of water movement, is increasingly being used for this purpose. However, analytical methods that are commonly used are limited by uncertainties in the effective thermal diffusivity of the sediments at the SW-GW interface. We present a novel 1-D analytical method. It utilizes both the amplitude ratio and phase shift of pairs of temperature time series at the SW-GW interface to estimate the Darcy velocity. This eliminates both the need to specify a value for effective thermal diffusivity and the need for iteration. The method also allows for an estimation of effective thermal diffusivity, which can indicate periods where assumptions to the analytical solution are violated. Riverbed temperature data from the Murray Darling Basin (Australia) are used to illustrate the method.