The ECU decides (based on various parameters) wether to turn the engine off or keep it running. Some of those are engine temp, AC engaged or not, heat on full blast, hybrid battery state of charge.
This engine is designed to do this and there is no reason to be worried about premature wear and tear. It is important to use the right oil however, Honda Green 5W20. It starts using the IMA motor so no wear on the starter. (Starter is there only as a back up for when the IMA system can't function for whatever reason)
If you are still concerned however you can keep the engine running by turning on the front defroster. It works even if you manually disable the AC and turn down the fan.
This engine is designed to do this and there is no reason to be worried about premature wear and tear. It is important to use the right oil however, Honda Green 5W20. It starts using the IMA motor so no wear on the starter. (Starter is there only as a back up for when the IMA system can't function for whatever reason)
If you are still concerned however you can keep the engine running by turning on the front defroster. It works even if you manually disable the AC and turn down the fan.
