I inherited an older Moccamaster, which does not have the timeout, and the newer one went straight to storage.
Unfortunately the old button without a timer is not sold as a spare anymore, or I would have "downgraded" the newer machine.
There are coffee machines that pour coffee straight into thermos.
I personally can't stand the taste of 'cooked' coffee. I'll grind and make another mug when needed in an espresso coffee maker. Doesn't take long at all. Mine is manual but you can have automatic machine to shave off even more time.
It flicks off every 40 minutes. Turning it on after 40 minutes will keep it warm as the hot plate has residual heat that keeps it piping hot for about 5-10 minutes fter it switches off.