I made a very lightweight 14th century cotte for my boyfriend for summertime. This is single layer linen. It's pretty simple, the most painstaking aspect being the fit, which I've already worked on with him in the past. This one is slightly less fitted than some of his other cotehardies/cottes, in consideration of warm summer weather.
He is also wearing tights I made for him, along with a black linen embroidered coif.
You can see more images here: http://www.faerie-queen.com/green-cotte/