Why does my extension cord get warm with a space heater but not with a kettle?

It’s the duty cycle, not the wattage. Both devices pull about 12.5 amps, but the heater runs continuously while the kettle runs for only a few minutes. Sustained current causes resistance heating in the cord, so a 14-gauge cord will get warm under a continuous 1500W load. A little warmth is normal, but if it’s uncomfortably hot, size up to a 12-gauge cord.