I come from a Polish family and a constant of every christmas is a spicy fermented beet soup. My family has been fermenting the beets exclusively in a terracota vessel on a hot radiator when the heating is on for the winter. That's the way my mum and grandma are doing it, and the way their mothers done it before them. They claim that it's imperative that the temperature of the vessel doesn't drop, cause that risks the entire batch going bad.
Now, that is pretty much against everything I read about temperatures and fermenting (i.e. colder is tastier and safer, warmer is more spoilage-proof). I mean, especially considering that food-on-a-radiator sounds like a danger zone party for the beets.
On the other hand, that is the traditional method, nobody ever got sick in my family and it does indeed not work out when done cold. I heard of warm fermentations being done in the context of brewing beer, but that's a different kind of fermentation so I'm assuming it's unrelated. So I'm pretty puzzled about this.