Not even that. His argument is it FEELS more like summer. Nobody can dispute that August has higher temperatures than May, but what use is slightly higher temperatures if it's cloudy/raining/windy/gloomy. Indeed, on occasion September can bring pangs of summer, but tends to require something a bit more 'special' to prevent temperatures falling away at night, mist/fog forming, and high enough temperatures in the day. For what it's worth, I don't think of September as a particularly settled month anyway. The Atlantic tends to pick up as August progresses anyway so it's quite difficult for September to reverse that trend.
Also, nobody is expecting a Mediterranean climate here. It would be foolhardy to do so. I would personally, however, expected something a bit more spectacular to have come from the most recent heatwave given the circumstances.