Mine is also run on the cold water line; however I do run about 30' of hose into my sump (coiled) before it reaches the unit. The water is warmer that way.
I've been told that cold water will lessen the life of the membrane.
Since I ran the extra line, i find my output is greatly increased as well.
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New 280 gallon inwall in planning stages;details, details, details. 
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