Once upon a time I carried a small rectangular sleeping bag in my car that had a fleece lining and nylon shell.
It was red, and came from Marlboro. I don't smoke but knew lots of folk who did and I "got the gear".
The nylon shell did indeed extend the temp rating quite a bit. I could unzip it to form a big blanket to cover two people, which was useful on several occasions.
One wintery November night I slept in it in the cab of a pickup truck when I simply couldn't stand the feller snoring to beat the band in a motel room on a job. I wore my insulated coveralls inside the bag and was quite toasty.
I slept in it several summer nights on the high prairie in Oregon when working jobs and the local motels were full. ( heh, ever try to get a motel when the Roundup is in town? ).
It was a very useful item, so naturally it was stolen out of my car one day.
I looked for a new one and discovered the few fleece bags with nylon shells were very expensive!
So I made a few of my own. These are specifically for keeping in a car and not backpacking ( although they would work fine ) so I don't mind the extra weight.
Also, it isn't a good idea to compress a sleeping bag all the time, but I don't think fleece cares so much, making it idea for long term storage in a car.
I was able to make 'em out of stuff I had on hand so the outlay was zero, which is also important for me.
My wife is a quilter and buys quilt batting by the roll, so what the heck, I put a layer of it inside as well. She also had salvaged a big pile of tulle from a wedding, so I sewed a generous roll of that to the top for use as a mosquito bar.
Goofy and heavy, but free and useful. The fleece certainly does make a nice warm inner layer!

I made it big and rectangular with a sewn on foot pocket. For storage the quilt folds into the foot pocket.

A smaller one being made –

I even used fleece for the bottom of our new home made sleep system.
Fleece on top –

It holds two thermarest pads in place. Very warm! The top quilt is held in place with velcro.

Dunno how helpful this is, but I thought I'd relay my experience wit just such a fleece / nylon shell sleeping bag.
Don't throw out all those old fleece throws people give you!
They are useful for projects.