A common myth says you shouldn't fry with olive oil. In reality, extra virgin olive oil has a smoke point of about 190-210°C, which is sufficient for most cooking methods.
Olive oil's high antioxidant content makes it one of the most stable oils when heated. Polyphenols protect the oil from degradation.
However, heating does reduce some aromatic compounds. Therefore, it's recommended to use higher-quality oil for finishing and a more affordable variant for cooking.