Your box fan is just burning off dust. That's normal.

That burning plastic smell is almost always just dust or lint burning off the motor or blades.

Box fans sit on the floor. They suck up dust, pet hair, and general household junk. When you first plug one in after it’s been sitting, the heating element (the motor) warms up and slowly incinerates all that crud. Smells like a cheap space heater or a vacuum cleaner that’s due for a filter change.

This is usually harmless. It should fade after a minute or two. If it lingers for more than 10 minutes, or if you see actual smoke, that’s a real problem — maybe the motor winding insulation is failing or the fan is overheating. In that case, unplug it and either clean it thoroughly (compressed air, wipe down blades) or just toss it.

Same goes for a brand new fan — the first few runs will cook off residual oil or manufacturing film. Open a window.

If it smells like burning plastic constantly, replace the fan. Don’t mess with a motor that smells like frying wire. Not worth the fire risk.