The invention provides methods and an apparatus for more efficiently and economically producing purified water from sea water or some other salty or brackish water source. The efficiency is derived from the co-location with a power plant or other thermal generating source that will heat the feed water. Reverse osmosis membrane filtration systems work optimally when the feed water is at certain higher temperature, where that temperature is typically higher than the feed water at ambient temperatures. By using the heated sea water as the byproduct of the power plant electricity generating process and if necessary mixing it with ambient temperature sea water, if needed to lower the water temperature, and using this feed water with a higher temperature than ambient water temperature, the efficiency of the reverse osmosis system can be increased.