Heat-conducting oil furnace is a widely used heating equipment in industry. The performance of heat-conducting oil furnaces is affected by different heat loads during the production process. To investigate the operational flexibility of a thermal oil furnace with a designed load of 25 MW and optimize its operating conditions, numerical simulations of the heat-conducting oil furnace are conducted using computational fluid dynamics under five different heat load conditions (30%, 60%, 80%, 100%, and 110%). In order to obtain a more detailed understanding of the flow and combustion characteristics of the heat-conducting oil furnace, the influence of different heat load conditions on the distribution of parameters such as velocity, temperature, and component concentration during the flow and combustion process inside the furnace are studied and analyzed. The current layout of the burner results in a high velocity difference between the high-speed fuel jet and the air, and there are clear boundaries in the area affected by the jet. The suction effect on the surrounding flue gas is significant near the burner. When the heat load exceeds 60%, the reflux area in the furnace is larger, the residence time of flue gas is prolonged, and the overall temperature in the furnace is higher, which is conducive to the heat absorption and temperature rise of the heat transfer oil in the furnace tube. Under full load and overload operation conditions, it is important to pay attention to the impact of higher flue gas flow rate and temperature on furnace tubes and other components and avoid problems such as convection chamber furnace tube vibration, local overheating, and even overheating caused by high workload. The above research results can provide theoretical guidance for the design and the operation of heat-conducting oil furnaces, which has practical significance.