I'd take the entire thing & set it up for serving as one piece as well. The liner would more difficult to carry by itself & outer part will act as insulation, I'm guessing....

I use a cast iron enamel Dutch oven....have the whole thing simmering, then find a cooler it will fit into and line it with about an inch of newspaper, and put a towel over the paper, your pot into the cooler, cover with the beach towel, more newspaper and shut the lid.
I have had soup and stew stay burn your mouth hot for more than 3 hours.
I have also used a covered casserole.
You could do the same thing with the liner of your crock pot....but I think a heavy casserole dish would look lots better on the serving table.
I have also stacked 8 1/2 by 11 pyrex casseroles in a cooler lined with newspaper and had it stay very hot for 3 or 4 hours....and I could take out one casserole, serve it and then get another hot one out.
I covered one casserole with foil, put a small cookie sheet on top and set the other casserole on that....covered with foil and then newspapers.

Linda's method is excellent. If you don't have the right size cooler (consider putting it on its side!), you can do the same thing with a cardboard box and many more newspapers and towels and/or blankets. The point is to have layers and layers with trapped air in between to insulate it, same as dressing to go out in the cold.

Yes...I have even done the cardboard box thing with a roaster with a turkey in it.
We used to have some killer tail gate parties!! LOL!

Once a year I would make 5 quiche bake them and when done stack them with a heavy pottery plate in between each pie and do the newspaper lined cooler thing. There was usually one quiche that hadn't been touched, and after the game we would snack on that....still very hot ( but the crust was a bit soggy) fully 8 hours after it had been taken from the oven.