When designing a reinjection scheme for geothermal development, one needs to predict the flow and thermal behavior between the recharge and discharge wells. Premature thermal front breakthrough is of great concern and is often observed in real fields. However, prediction methods based on homogeneous media are prone to overly optimistic estimates. In this study, geothermal reservoirs with vertical fractures which are discretely distributed in the permeable rock are considered, and the streamline simulation is developed and applied to evaluate the thermal front movement, represented by the characteristic times tD*. With 1000 simulation results for stochastically generated natural fracture systems, regression models are developed for the expected values of tD* with minimal information requirements on fracture parameters. In general, the fracture orientation θf has a stronger negative correlation with tD* than the total fracture length Σf. The intensity of natural fractures has opposing effects (delay or advance) on tD* depending on θf, and taking this effect into account improves the quality of the regression model. In addition, when the pressure difference between the doublet wells is available, the model accuracy is further improved by incorporating pressure data into the regression. The prediction models are of practical use for understanding the thermal behavior and designing a reinjection scheme in fractured geothermal reservoirs.