In August Milan is not at its best: usually temperatures are very hot (yesterday afternoon temperatures in town were in the range of 38-39 °C) but at least is not crowded because 15th August is the peak day of the holiday season, so the locals are not in town and all the people you will see around are probably tourists. On the negative side expect reduced public transportation service.

Anyway I hope you will enjoy you trip to Milan, and if you need any suggestion feel free to PM me.