I only just caught your post, missed it entirely somehow.
To the first question, my own answer is that the thermostat serves to optimize cabin heating and that the engine is pretty indifferent to its presence or absence.
As to installation, that's fairly self-evident if only the bellows are concerned, one end if fixed to a stirrup that goes in the casing top adjustment slot, the other end goes on the flap operating arm through the slot at bottom of the casing.