Can I plug a space heater into an extension cord?

Don’t. A 1500W space heater pulls about 12.5 amps, and even a heavy-duty 12-gauge cord is a fire risk if coiled, pinched, or under a rug. Most extension cords aren’t rated for continuous high-draw loads. If you absolutely must, use the shortest, thickest cord you can find (10 or 12 gauge, no longer than 25 feet) for a few minutes only—but move the heater closer to the wall outlet instead.