The external bypass valve is set by:

The external bypass valve is set by determining the temperature rise across the appliance. This is critical because the bypass valve is designed to maintain appropriate temperature levels within the system, ensuring it operates efficiently and safely. By assessing the temperature rise, the technician can adjust the bypass valve to achieve the desired operational parameters, which helps in optimizing the appliance's performance and preventing problems like overheating or insufficient heating.

Proper settings of the bypass valve based on temperature rise also contribute to energy efficiency. If the temperature rise is too low, it might indicate that the valve needs to be adjusted to allow more flow through the appliance, whereas a high-temperature rise might suggest that the flow is restricted more than necessary. This approach ensures that the appliance runs within its optimal temperature range, thereby enhancing safety and longevity.

The other options do not directly relate to the specific use and adjustment of the external bypass valve as effectively as the temperature rise. Shutting off the pump, observing the burner flame size, and determining the appliance input all provide important operational insights but do not specifically guide the setting of the bypass valve in relation to the appliance's thermal performance.