An oil supply system for a gas turbine engine has a lubricant pump delivering lubricant to an outlet line. The outlet line is split into at least a hot line and into a cool line, with the hot line directed primarily to locations associated with an engine that are not intended to receive cooler lubricant, and the cool line directed through one or more heat exchangers at which lubricant is cooled. The cool line then is routed to a fan drive gear system of an associated gas turbine engine. A method and apparatus are disclosed. The heat exchangers include at least an air/oil cooler wherein air is pulled across the air/oil cooler to cool oil. The air/oil cooler is provided with an ejector tapping compressed air from a compressor section to increase airflow across the air/oil cooler.