varroa fall through the mesh and die we hope
Its not quite that simple.
But that is the idea our chums in the colonies use {ADDED - a similar floor but with} a slightly wider mesh and a shallow dish of cooking oil beneath - to trap Small Hive Beetles. The beetles can't maintain a large population because they fall through the holes - and die.
Unfortunately, Varroa don't accidentally fall through in big enough numbers to control the population.
But the mesh floor allows varroa population monitoring (by observing the
natural death rate).
And if any live ones fall through that's a (tiny) bonus.
The bees are pretty good at temperature regulation. At least in the UK's climate - Summer max to Winter minimum ... I accept that its different in Finland, where it gets REALLY cold.
The bottom ventilation reduces damp problems (and associated diseases).
Its really only for wax-drawing in bad weather that every little bit of hive-warming helps.
The mesh floor makes for a healthier hive, and allows Varroa monitoring.
First introduced in the UK mainstream? About 20 years ago.