What gauge extension cord should I use for a 1500W space heater?

Use 12-gauge, not 14-gauge. A 1500W heater draws 12.5 amps, and 14-gauge is rated for 15 amps but derates to only 12 amps for continuous loads — so you’re already over. A 12-gauge cord handles 20 amps (16 amps derated), giving safe headroom. Don’t risk a fire to save ten bucks.