A method and apparatus for cooling chips on a computer memory module. The apparatus includes a primary and secondary heat spreaders, at least a first heatpipe coupled to the primary heat spreader and having a remote portion spaced apart from the primary heat spreader and thermally contacting the secondary heat spreader, and a coolant within the first heatpipe and the primary heat spreader so as to absorb heat from the primary heat spreader and conduct the heat to the secondary heat spreader. The primary heat spreader has at least two panels configured to engage the memory module therebetween, with facing contact surfaces of the panels adapted for thermal contact with the module chips. The secondary heat spreader is configured to increase surface dissipation of heat from the first heatpipe into the environment. The coolant has a boiling point at or below a maximum preselected operating temperature of the module chips.