AbstractGeothermal systems in amagmatic orogens involve topography‐driven infiltration of meteoric water up to 10 km deep into regional‐scale faults and exfiltration of the heated water in surface springs. The thermal anomalies along the upflow zones have not been quantified, yet they are key to estimating the geothermal exploitation potential of such systems. Here we quantify the three‐dimensional heat anomaly below the orogenic geothermal system at Grimsel Pass, Swiss Alps, where warm springs emanate from an exhumed, fossil hydrothermal zone. We use discharge rates and temperatures of the springs, temperature measurements along a shallow tunnel, and the formation temperature and depth of the fossil system to constrain coupled thermal–hydraulic numerical simulations of the upflow zone. The simulations reveal that upflow rates act as a first‐order control on the temperature distribution and that the site is underlain by an ellipsoidal thermal plume enclosing 102–103 PJ of anomalous heat per km depth. When the fossil system was active (3.3 Ma), the thermal plume was double its present size, corresponding to a theoretical petrothermal power output of 30–220 MW, with the 120 °C threshold for geothermal electricity production situated at less than 2‐km depth. We conclude that mountainous orogenic belts without igneous activity and even with only low background geothermal gradients typical of waning orogens are surprisingly promising plays for petrothermal power production. Our study implies exploration should focus on major valley floors because there the hydraulic head gradients and thus upflow rates and heat anomalies reach maximum values.