Abstract: An offset gearbox of an aircraft has a sump for a lubricant. A heat exchanger core extends through the sump in contact with the lubricant. A fluid coolant for cooling an accessory such as an electrical power generating unit drivingly connected to the offset gearbox is circulated through the core in thermal communication but not mixed with the lubricant of the offset gearbox for cooling the lubricant. The cooling arrangement for the offset gearbox advantageously does not require a separate or dedicated heat exchanger which reduces system weight and cost. The single pump of the accessory can also be used for circulating the coolant. Increased reliability, independent oil change for maintenance and enhanced attitude performance are attained as gearbox performance does not affect power generating unit performance, and visa versa. An existing aircraft can be modified to include the offset gearbox with a minimum of modification and little additional weight and plumbing.