Systems and methods of cooling a motor of an electrical submersible pump (ESP) assembly employed in an electrical submersible subsea booster pumping system, are provided. A supporting frame structure such as an ESP mounting skid or top end assembly of a caisson having structural members exposed to environmental seawater, is modified or designed to include fluid conduits within the structural members to establish lubricant pathways for lubricant to flow. A heated/hot lubricant line connects between a supporting structure lubricant inlet port and an ESP motor lubricant outlet port. A cooled lubricant line connects between a supporting structure lubricant outlet port and an ESP motor lubricant inlet port. A pump or other fluid moving device circulates lubricant from the ESP motor to the lubricant pathways within the supporting frame structure, whereby the seawater cools the lubricant contained therein, which is then circulated back into the motor to assisting cooling the motor.