I don't know much about space heaters but we use a programmable thermostat and it's set to bring the house to the temp we want when our alarm clock rings. That isn't really what you were looking for but maybe if another member of your household wakes up earlier, you could ask if he/she can do it?
Another option would be to find a space heater that has a two position switch, set it to the on position, and plug it into a timer. My parents did this with coffeemakers waaay before coffeemakers had built in clocks & brew times. This was with an old percolator. Anyway, just make sure that the timer is rated for the amount of watts/amps you'd be running through it, not a simple lamp timer. Not worth starting a fire over it!
I mention the 2 position switch because things like modern TVs that use the same button to turn off and on, don't work well with timers. The device that you're trying to regulate needs be able to be left in the on position for the timer to function as the switch.