There’s no difference between the storage of the image and the base filesystem of the container, the layered FS accesses the images layers directly as a RO layer, with the container using a RW layer above to catch any changes. Therefore your goal of having the container running in memory while the Docker installation remains on disk doesn’t have an easy implementation.
If you know where your RW activity is occurring (it’s fairly easy to check the docker diff of a running container), the best option to me would be a tmpfs mounted at that location in your container, which is natively supported by docker (from the docker run reference):
$ docker run -d --tmpfs /run:rw,noexec,nosuid,size=65536k my_image