Diagnosis
This is normal. It's dust and manufacturing residues (like oils from assembly) burning off the ceramic heating element and internal components.
How to Fix It
Run the heater on its highest heat setting in a well-ventilated room for 30-60 minutes. Keep it away from smoke detectors. The smell should dissipate completely after a few cycles.
If That Didn't Work
If the smell is acrid, persistent, or accompanied by visible smoke, unplug immediately. There could be a wire insulation issue or a plastic component touching the element. This requires internal inspection.
Heads Up
Do not mistake a dusty smell for the new heater smell. If you didn't clean it before storage, dust buildup will burn off and smell every season. Clean the interior first.