That’s pretty clever.
The place where LENR stands in that analogy is that water turns to gas through evaporation at lower temperatures so maybe you can just distill that vapor in smaller amounts.
That actually is "a thing" in chemistry. Called "sub-boiling distillation". Elimination of bubble formation and subsequent breaking drastically reduces contaminant carry-over and yields a much purer final distillation product. Used primarily in the production of ultra-pure reagents for ultra-trace analysis.