Abstract Accurate and efficient simulation of fluid and heat flow in fractures has long been a topic of interest for fractured reservoirs, e.g., enhanced geothermal systems (EGS) and unconventional oil/gas formations. In this paper, we propose a flexible and effective modeling approach, the extended embedded discrete fracture model (XEDFM), to simulate fluid and heat flow in fractured reservoirs with 3-D non-planar fracture networks. Compared with the conventional embedded discrete fracture model (EDFM), the XEDFM possesses two major merits: (1) separation of fracture discretization and matrix gridding provides maximum flexibility in handling fractures with complex geometry/topology, regardless of the resolution of the matrix grid; and (2) the combination of connection-list strategy and the concept of non-neighboring connection facilitates the construction of fluid-heat flux between the fracture and the matrix/fracture. With systematically validated XEDFM, the impacts of fracture roughness and heat extraction strategy on hydrothermal behaviors and heat mining efficiency are investigated. Another example introduces a workflow for design and modeling of 3-D non-planar fracture networks, with which the performance of horizontal and vertical wells in tapping heat energy from EGS are explored. This work presents a flexible and effective approach for modeling fluid/heat transfer accurately in 3-D non-planar fractures, and provides a set of framework and efficient algorithms for non-planar fractures design, discretization and simulation, establishing the foundation to build and simulate models with complicated fractures.