How to line a denim jacket.?

I have a denim jacket. It is VERY plain. By that I mean a single layer of denim. I took it to school today in 50 degree weather. Surprise! It wasn't NEAR warm enough. So, I am wondering how I would go about lining this jacket with something to improve its quality of retaining warmth. Would I use a "fake fur" or "fake fleece" or something like that to line it? Or would I use something else? Also, how would I go about doing it? Would I sew it in? Would I make it removable? Looking for a good answer, so please, please help the poor cold child. xD