Most heaters on high are 1500W. That's close to 13A depending on your line voltage. They are not designed for continuous use. This power will make the line cord (HPN typ.) get warm to the touch. The blades on the power plug will be very warm to touch as well under long runs with this power draw. Also be aware that most receptacles employ series/parallel wiring so if you're plugging in to a receptacle at "the end" of the line, many other sockets - even if not in use - can be a cause of heating and reduced line voltage. A simple check with a forward looking infrared radiometer (FLIR) will reveal hot receptacles. Back wired ones are frequent offenders. Also, improperly terminated aluminum wiring will cause heating.
Heater coils on old units (bare nichrome ribbons or coils) on high settings could glow cherry red. Usually fan forced heaters with reduced airflow will have coils glowing brighter. They will burn out fairly quickly if left running like this. The mica insulators will also degrade faster and if the coil touches the chassis and shorts it will glow white hot and spark all nice and hopefully no one has put a penny under the fuse!
Ceramic heaters do not glow at all and should be kept free of dust and other debris. These types like the original Pelonis disc furnace had foam filters that needed to be cleaned.
They also had very high inrush current and could pull 25A or more for a few seconds when cold started. This would blow non slow blow fuses if the circuit was protected by them which was a pita.