We present three‐dimensional numerical simulations of natural convection in buried, vertical en echelon faults in impermeable host rock. Despite the fractures being hydraulically disconnected, convection within each fracture alters the temperature field in the surrounding host rock, altering convection in neighboring fractures. This leads to self‐organization of coherent patterns of upward/downward flow and heating/cooling of the host rock spanning the entire fault array. This “synchronization” effect occurs when fracture spacing is less than the width of convection cells within the fractures, which is controlled by fracture transmissivity (permeability times thickness) and heterogeneity. Narrow fracture spacing and synchronization enhance convective fluid flow within fractures and cause convection to initiate earlier, even lowering the critical transmissivity necessary for convection initiation. Heat flow through the en echelon region, however, is enhanced only in low‐transmissivity fractures, while heat flow in high‐permeability fractures is reduced due to thermal interference between fractures.