A new recovery process, thermal-assisted gravity drainage (TAGD), is described for the recovery of bitumen from heterogeneous carbonate reservoirs. The process is shown to be thermally efficient in lower-porosity formations and is less impacted by the complex porosity distributions, that characterize carbonate rock. The TAGD process heats the reservoir by means of a pattern of horizontal heater wells to allow bitumen to flow by gravity into a producer placed at the base of the reservoir. High thermal efficiency is achieved by heating the reservoir to 120-160 degrees C. The energy for this process is transferred to the reservoir by heat conduction from electrically heated mineral-insulated cables. Precise control of reservoir heating is accomplished by optimally placing heater wells within the formation and adjusting the power in each heater for efficient energy usage. Voidage replacement is achieved by solution-gas evolution and connate-water vapourization. The target of this new technology is the thick, highly permeable, and vertically continuous Leduc bitumen reservoir located in the Liege area of north-central Alberta. In addition to improved energy efficiency, the TAGD process does not require water for steam generation, thus reducing the size and initial capital cost of the surface-processing facilities.