Which control operates the oil burner during summer for domestic hot water needs?

The aquastat is the correct control that operates the oil burner during the summer months to meet domestic hot water needs. An aquastat is designed to monitor the water temperature in the heating system and activate the burner when the water temperature falls below a predetermined set point. This functionality is particularly vital for maintaining hot water during the summer when heating demands are typically lower. By regulating the temperature, the aquastat ensures that household hot water requirements are met without unnecessary heating, which would be inefficient and could lead to wasted energy.

The other options do not serve this function effectively. A pressure relief valve is a safety device that prevents excessive pressure in the system but does not control the burner. A vaporstat is primarily used in systems that utilize vaporized fuels and manages the vapor pressure, but it is not directly responsible for operating the burner for hot water needs. A temperature gauge simply displays the current temperature of the water but does not control the burner operation.