Is an underrated extension cord a fire hazard?

Yes. If the cord can’t handle the power draw, it heats up and can cause a fire. Check the device’s label for watts or amps (divide watts by 120 for amps), then match or exceed the cord’s rating. A space heater pulling 12-15 amps needs at least a 14-gauge cord, preferably 12-gauge. Don’t guess—buy a heavy-duty cord rated for 15 amps or more.