Which portion of a typical downflow-type radiator is the warmest when the engine is at operating temperature?

In a downflow-type radiator, the warmest section when the engine is at operating temperature is indeed the top tank. As the engine runs, the coolant circulates through the engine, absorbs heat, and then enters the radiator. Gravity causes the coolant to flow downward through the core tubes, where it is cooled by the airflow as the vehicle moves or by the operation of the cooling fans.

Since the coolant enters the radiator from the engine at a high temperature, the top tank, which receives the hot coolant first, will be the hottest section of the radiator. The coolant then cools as it flows downward through the radiator core and eventually collects in the bottom tank, which is considerably cooler than the top tank. The surge tank, while part of the cooling system, is used for overflow and pressure management rather than being a direct part of the heat exchange process within the radiator, and thus it doesn't reach the same high temperatures. The center of the core does experience heating, but it is the top tank that consistently maintains the highest temperature due to its direct connection to the incoming hot coolant.