July 29th-August 15 Should I wear a cotton-padded jacket around Melbourne and Sydney, Australia?

I don't think so. A thick sweater is enough, but Sydney is warmer than Melbourne. If it rains, it's still cold, especially in Melbourne. I checked. According to the weather forecast, there will be moderate rain at 8- 10℃ in Melbourne on the 29th, and light rain at 15-22℃ in Sydney on the 29th. This is for reference only, but the weather is constantly changing. Pay more attention to the weather and bring some thick clothes.