Just a thought, although it isn't "cool". I like simple, cost-effective solutions. Elegance comes in third.
If it's a 10x10 or 12x12 room, you can put a quartz or ceramic heater with fan/thermostat in there and have all you need for functionality.
I have one of these in my office out behind the garage. The space is heated/air conditioned through the house system but it's on a slab and it gets cold in the winter. This thing totally solves the problem... for $40.
As a bonus, you can tailor the temperature in the baby's room to any level required, either cooler or warmer than the rest of the house.
800-watt and 1500-watt heat settings plus cool fan setting
Oscillates 60 degrees
4-hour timer can be set in half-hour increments
Instantly shuts off if it's tipped over
Top-mounted control panel with soft-touch controls and LEDs to show settings
Full-function remote control turns power on and off, controls heat settings, selects the fan function, sets the timer and controls oscillation
Stands 32" tall and aprox 9" wide by 9" deep