Abstract Streamline-based simulation is extended to simulate non-isothermal two-phase flow of hot water injection in three-dimensional (3D) realistic field-scale reservoirs containing heavy oil. First the pressure equation is solved on the 3D Eulerian grid for a global time-step and the total velocity is calculated at cell faces. Then the streamlines are traced from injector wells to producers, implementing a semi-analytical method and the time-of-flight (TOF) is computed over the streamlines. The mass and energy transport equations are mapped onto streamlines using the TOF as the distance variable. The advective part of the transport equations are solved along the streamlines. The saturation and temperature are calculated in the TOF domain until the end of the global time-step and then mapped back to the 3D grid. The effects of gravity and heat conduction are included by an operator splitting technique, at the end of each global time-step. A 2D petroleum reservoir model without gravity is tested to show the feasibility of the method. To further test the approach, a 3D heterogeneous model with a fine grid and multiple wells is simulated, and the results are compared with those of a commercial grid-based thermal simulator. The predicted saturation distribution, temperature and oil production at the wells are in good agreement with the commercial code; furthermore the streamline technique is significantly faster while generating results similar to those obtained using a conventional method that has a finer grid. We conclude that the streamline method can simulate non-isothermal two-phase flow of water–oil in heterogeneous porous media accurately with lower cost and better performance than grid-based approaches.