It's the duty cycle, not the wattage.

The cord gets warm because the heater runs continuously, while the kettle only runs for a few minutes at a time.

Both devices pull about 12.5 amps on a standard 120V circuit. A 14-gauge cord is rated for 15 amps, so it’s technically fine for either one. But sustained current causes resistance heating in the cord itself. Run a 1500W heater for two hours straight and that cord will be noticeably warm. Run the kettle for four minutes and the cord hardly has time to get above room temperature before you pour the water.

This is normal. 14-gauge is the minimum for 15 amps, and it will get warm under a continuous load. If the cord feels hot enough to be uncomfortable to touch, or if you’re running it through a tight coil, size up to a 12-gauge cord. But a little warmth is just physics doing its job.

It’s also worth knowing that many space heaters are designed to run at the ragged edge of the circuit, so they’re extra sensitive to any voltage drop in an extension cord. Kettles don’t care as much because they’re on and off before the heat builds up.