The Puga geothermal reservoir is located in the south-eastern part of Ladakh (Himalayan region, India), and it is providing encouraging results towards heat production. We proposed an improved mathematical model for the fully coupled thermo-hydro-geomechanical model to examine the variations in the Puga geothermal reservoir at between 4500 m from the surface with three, four, and seven hydraulic fractures in the reservoir along with four-spot, five-spot, seven-spot, and nine-spot well patterns. The distribution of low-temperature region is found in each fracture, and it is low in the reservoir with seven hydraulic fractures. The changes in the rock and fluid properties are examined effectively. Thermal strain is dominated in the fractures, and mechanical strain is impressive in the rock matrix; it is dependent on the number of hydraulic fractures and well patterns. The thermal performance of the Puga reservoir is examined with the geothermal life, reservoir impedance, and heat power and found that the number of hydraulic fractures and well patterns are influenced significantly in the multistage modeling of the Puga geothermal reservoir. Thus, the proposed mathematical model can effectively evaluate and predict the variations that occur in the Puga geothermal reservoir with dynamic rock, fracture, and fluid properties.