Where I live, the heat reaches its peak in August.
Does it get cooler in Beijing, China in August?

I think it is same here in Beijing!

By the way, East Asians who traveled to Bangladesh said that there are no Botanical Garden within the city where one can enjoy the beauty of nature.
Is it true?

No, it is not true. There is a large botanical garden in Dhaka city. It is located in Mirpur 2, just beside the national zoo.