Diagnosis
A burning smell during the first few uses of a new heater, or the first use after a long storage, is usually just dust burning off the heating elements and fins. A persistent plastic smell could indicate something more serious, like a wire insulation issue.
How to Fix It
For a new heater or one coming out of storage: Unplug it, take it outside or to a well-ventilated area like a garage, plug it in, and run it on High for 30-60 minutes. This will burn off any manufacturing residues or accumulated dust. The smell should dissipate. Make sure you've vacuumed the fins as described in the cleaning question first.
If That Didn't Work
If the plastic/burning smell is strong, persistent, or accompanied by smoke, unplug the heater immediately and do not use it again. This could indicate an electrical fault inside. Contact Pelonis support for guidance; the unit may need inspection or replacement.
Heads Up
Never ignore a strong, acrid electrical burning smell or visible smoke. It's different from the mild dusty smell of initial burn-off. In that case, shut it off, unplug it, and get it checked out.