I hadn't thought of that. Very elegant. One study found that the uranium absorption was much faster in warm/hot water. The reaction was 2x faster in 40C water than in 10C water. RO desal brine is usually warm, but steam distillation desal brine would be quite hot. To reduce its negative environmental impact, the hot brine is usually diluted and cooled in retention ponds before discharge. These ponds would be perfect for this uranium extraction process.
Night is when you let capillary action carry away the concentrated brine, preparatory to next day's further desalination. Pure water from day may be banked, meantime.
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5706215/figure/...