When your heater smells like melted or burnt plastic it could be dust and debris accumulating on the heating element or something plastic may have gotten lodged in the heater.
Other reasons for a heater smelling like melted or burnt plastic are faulty wiring, loose wiring connections overheating components and if it's a new heater the burning plastic smell could be the protective coating burning off.
If your heater is clean and free of any dust on the heating element it could be a loose or bad wiring connection or a wirenut is loose on heater.
If the burning plastic smell goes away pretty quickly then the heater is likely safe but if the burning plastic smell persists with your heater you should shut it off and have it checked out to be safe.
It is normal for an electric heater and even a gas heater or furnace to smell burnt when you first turn it on after it has not been used for awhile.
When an electric heater and other heaters sit unused for awhile it can accumulate dust and when you turn the electric heater on the heater can emit a burning smell due to the dust being burnt off.
This is normal and should go away within 10 minutes to 30 minutes or so but if not then it could be a sign that the heater and especially if it's an electric heater is bad and needs repaired or replaced.
Even a brand new electric heater or other heater including a gas heater may smell burnt for a bit when first turned on due to protective oils and paint during the manufacturing process.
But the heater and electric heater should not keep smelling burnt for too long or it's a sign that there's a problem which could result in a fire.
The burnt smell of the electric heater when just due to dust or the newness should fade away after a couple of minutes to a few hours and if not it could be a more serious issue.
A burning electrical smell is a more serious issue and can indicate overheating, damaged wiring or other electrical problems.
If you continue smelling burnt electrical smells it the heater should be turned off and unplugged or power cut off to it.
My electric baseboard heaters will emit a dust burning smell at the start of the season when I turn them on for heating as there can be dust that I cannot fully get out but it eventually burns off.