I will be touring China in May and June...Beijing to Hong Kong!

Yes, according to the previous weather statistics, the climate will be warm in that two months. T-shirts, long sleeves and other summer clothes are enough for you to prepare. Notably, remember to prepare rain gears because there may have many rainy days in HK in June.

In addition, you don't need to bring many formal clothes.
However, while visiting some museums, memorial halls, or churches, you are not allowed to wear shorts, slippers, or vests, such as Chairman Mao Memorial Hall, St.John's Catheral, and St. Joseph's Church. Thus you should pay special attention to these occasions.