Diagnosis
A brief, mild smell when first used each season is often just dust burning off the heating element. A strong, persistent plastic smell is not normal and points to something overheating that shouldn't be.
How to Fix It
First, unplug it and let it cool completely. Use a can of compressed air to blow out any dust through the rear air intake and front grille. If you can see dust on the ceramic heating element inside, that's the culprit. The smell should go away after a few minutes of operation on high in a well-ventilated area.
If That Didn't Work
If the burning plastic smell is strong and continuous, immediately turn it off and unplug it. A wire insulation or a plastic component inside is likely touching the heating element or a hot surface. This requires opening the unit to inspect for melted wires or damaged components.
Heads Up
Never ignore a strong, continuous burning smell. It's the main warning sign before a component fails completely or, in the worst case, creates a fire hazard.