Tempurature does affect sperm count, viability, and motility. This knowlege is not new.
This answer comes from www.tiscali.co.uk/lifestyle/healthfitness/menshealth/part1_4-1.html
“Even taking a hot bath (43-45°C/110-115°F) for half an hour per day can significantly lower sperm counts as can wearing tight underpants or athletic scrotal supports. This was shown in a recent experiment where the fit of a man’s underwear and its effect on spermatogenesis was investigated.”
According to the site above, sperm counts returned to normal. How long it takes depends on many factors - anywhere from 2 weeks to about 6 months.
I have not found any cite that shows hot baths will get the sperm count to zero, or even close to it. It will lower the sperm count and for a man with borderline fertility it can cause problems with conception.
I would imagine that the medical term for couples who use this method exclusively is “parents”.