Trefoil buried cable is one of the important cable arrangements for the underground transmission line, and its heat transfer performance is relatively poor. By filling with fluidized thermal backfill material (FTB) around trefoil buried cables, the heat transfer would be efficiently enhanced, while the filling cost should also be considered. In the present study, the heat transfer process in the FTB trefoil buried cables is numerically studied, where the cable core loss and eddy current loss in the cable were coupled for the simulation. The heat transfer performances and ampacities for trefoil buried cables with different back fill materials were analysed and compared with each other. Then, the laying parameters for the parabolic-type FTB trefoil buried cables were optimized with the radial basis function neural network (RBNN) and genetic algorithm (GA). Firstly, it is found that, with FTB material, the maximum temperature in the cable core is obviously reduced, and the cable ampacity is greatly improved as compared with the cables buried around natural soil (NS). Secondly, when compared with flat-type FTB model, the heat transfer rate in the cable with parabolic-type FTB laying method would be slightly reduced, while the FTB amount used for the buried cables is greatly reduced. Finally, as for parabolic-type FTB trefoil buried cables, with proper design of geometric parameters (s1 = 0.290 m, s2 = 0.302 m, and l = 0.3 m with I = 1300 A) for the FTB laying cross section, the overall performance for the cable was optimized.