I would imagine
that this is a peculiar
object, and one which is rapidly falling into disuse
at that. However, for the sake of posterity
I shall write about the tea cosy.
It is in fact nothing more complex than a cover for a teapot. Usually made out of thick knitted wool and shaped to fit, you would put the tea cosy over the teapot in an attempt to prevent it cooling down, so that your tea stayed hot for longer. Most tea cosies had a hole for the spout so that tea could still be poured whilst the cosy was in place, however some cheap and inferior products had no spout-hole and required removal of the cosy before more tea could be poured.
I personally always associate tea cosies with grandmothers and I think their glory days were before World War II. As a slang term "tea cosy" is sometimes used to describe the sort of hat -- again usually worn by old ladies -- which is thick, kintted and shapeless, as in "That old Mrs Wormley, whenever she goes up the Post Office to collect her pension she's got a tea cosy on her head".