I am thinking about constructing a tube to suck hot air from near the
ceiling of a high-ceiling room and reintroduce it and mix it with the
colder air at floor level. I have seen these things at work in other
buildings but I do not know what they are called.

I would like to read a bit more about them and find out if any
improvements from mixing hot air into the cold are worth the effort
but I am stuck by not knowing a suitable search term.

Any suggestions. please?

Nick