The following is excerpted from my response to an email question from a sewing pal.  The context is that age-old question:  When constructing a supportive cote (Gothic Fitted Dress, Versatile Dress), should it be lined?

My reading says that we don’t have extant ones that are lined.  We have
illustrations of ones with another color on the inside, but there’s a
popular medieval fabric weave (iridescent twill) that is one color on each side, so that
could be that answer.

My answer is ‘do what works’.  My blue linen cote isn’t; but my figure
is very different from other ladies who wouldn’t dream of not lining. We don’t have surviving linen female cotes.  I think a wool lining on
a wool cote would be more successful than two linen layers, because the
wool will felt to itself over time, and the linen will just stretch on
the bias differently.

Why is my answer ‘do what works’?  Because this is a game.  People who
lived at our latitude didn’t wear cotes, so it’s a nonissue.  If I want
to wear a cote here, it will be made of linen with a wool overdress,
because the climate dictates that choice, and I don’t have that much tropical
weight wool yet.   Because I am slender, and because I’m for damn sure
going to wear a proper shift underneath, I don’t bother lining.

Do I think a non-lined cote on a full figure with no shift will look bad?  YES.  Will a wool cote, regardless of lining, look good on any figure worn with a full shift?  YES.  Pick something in between those two.

(Related: Do I know how to deal with that annoying bias stretch differential between two linen layers that are sewn closed all the way around?  NO, and that’s one big reason I don’t do it.  The sag looks bad.)