Ding! We have a winner!

If you want the box to shutdown and immediately come back, you can use some variant of reboot. If you want it to shutdown and then come back at a later time, you're SOL without special hardware or a human standing next to the box.

If you wanted to get wacky, you could have the box reboot into some kind of not-entirely active state, like single user mode, wait for a pre-determined amount of time, and then boot into the normal fully-active runlevel. You better be damn sure of yourself though, because if you make a single mistake, it won't come back and you'll need someone to debug it from the console.

Or, more sanely, you could reboot but disable whatever services you don't want running until the time has passed. EG If the reason you want it "off" for a while is to keep people from surfing your web server, disable the web server daemon, reboot, wait until the time is passed and then start the web server.