The sustainability of geothermal fields is based on a paradox. On one side, fractures are targeted on heat-flow improvement, and on the other side, the same fractures are avoided because of induced seismicity risk. In this context, we developed analytical approaches for estimating (1) thermo–poro-elastic stresses in a fractured geothermal system, and (2) seismicity rates based on the model of Dieterich (J Geophys Res 99:2601–2618, 1994). We modeled cold water injected at a constant rate into a single fracture surrounded by hot impermeable layers. The rationale for focusing on one single isolated fracture was that flow in the vicinity of injection wells is often concentrated in a couple of fractures instead of being homogeneously distributed. Heat flow appeared to be dominated by advection inside the fracture and conduction outside it. Poro- and thermo-elastic stresses around the single fracture were estimated separately following two independent analytical approaches; and for any potential fault around the single fracture, the induced Coulomb stress rates were resolved. The role of thermal stresses appeared to be the leading one. We show that thermal-stressing rates can induce an increase in the rate of seismicity of more than a 1000-fold at distances up to 200 m from the single fracture. Our fast forward models are suitable for data assimilation and they open the route for heat-flow optimization while keeping seismicity at a relatively low magnitude.