Diagnosis
This is a serious warning sign. The motor is overheating or an electrical component on the logic board is failing. Continuing to use it risks a fire.
How to Fix It
Disconnect power to the opener immediately at the circuit breaker. Do not use it. The most likely cause is a failing motor capacitor or a seized motor bearing creating excessive load. Both require professional diagnosis and repair.
If That Didn't Work
If the smell is more plastic-like, inspect the wiring harness where it connects to the logic board. Look for melted insulation or a burnt connector. This indicates a short circuit.
Heads Up
This is not a DIY fix if you smell burning. The risk of electrical fire or shock is high. Contact a qualified technician. Do not reconnect power until it is inspected.