The determination of thermal diffusivity is a pre-requisite for geothermal site characterization and utilization. The temperature recovery (TR) method is a popular method for determining in-situ thermal conductivity together with the thermal response test and thermal conductivity probe methods. To determine in-situ thermal properties of the subsurface following a thermal disturbance produced by drilling processes or a heating cable within a borehole, the TR method is used to record decaying temperatures during the recovery period. However, to date, no studies exist to determine thermal diffusivity using up-welling water within a well. In this study, we introduce a 1D numerical method for estimating in-situ thermal diffusivity of the subsurface using up-welling thermal water as a heat source within an artesian well. Our numerical model includes parameters for the position of a sensor within a borehole, as well as for the thermal properties of a well casing and an annulus. Two data sets from the scientific literature were used to verify our model. Field data from the Jiashi Hot Spring in Taiwan were also used to demonstrate model suitability. Our model's value for thermal conductivity is consistent with the range of values for saturated sand within the scientific literature. Accuracies for thermal diffusivity estimations under short disturbance/recovery period were also evaluated. The results suggest that in-situ thermal diffusivity can be accurate determined, with an error less than 10%, using a short testing period with pumping time as low as four hours and a recovery of 24 h.