Circulating groundwater transports heat. If groundwater flow velocities are sufficiently high, most of the subsurface heat transport can occur by advection. This is the case, for example, in the Cascades volcanic arc where much of the background geothermal heat is transported advectively and then discharged when the groundwater emerges at springs. The temperature of spring water can thus be used to infer the geothermal heat flux. If spring water temperature is many degrees warmer than the ambient temperature, as it is at hot springs, determining the heat discharged at springs is straightforward. At large-volume cold springs, however, the geothermal warming of water is small because the added heat is diluted in a large volume of water. We show that in order to interpret the temperature of cold springs we must account for three processes: (1) conversion of gravitational potential energy to heat through viscous dissipation, (2) conduction of heat to or from the Earth's surface, and (3) geothermal warming. Using spring temperature data from the central Oregon Cascades and Mount Shasta, California, we show that the warming due to surface heat exchange and dissipation of gravitational potential energy can be comparable to that due to geothermal heating. Unless these confounding sources of heating are taken into account, estimates of geothermal heat flux derived from temperatures of cold springs can be incorrect by large factors.