Does shutting off my gas fire when I'm away from it for a short while save energy?

I sit and read by my fire at various times throughout the winter day. Sometimes I am leaving it for only 15 minutes or so. If I am doing something else for longer, I definitely turn it off. Does shutting it off during the shorter periods and then turn it back on, save or expend more energy?

(Sending this to our BTU Guy who will probably have a field day.)