It depends on your intended destination. Some regions of Dubai are more traditional than others. When you're in Jumeirah or Downtown Dubai, you will see more casual attire. In certain areas of old Dubai, such as the Spice Souk, it is prudent to dress modestly. Dubai's summer months can get up to 55°C/121°F.
Extremely oppressive heat can make it very difficult to breathe.
You should wear cotton garments that are light and breathable because you will sweat profusely! Since it is so hot outdoors, all the inside places have their air conditioning on full blast, making them feel extremely chilly.
While viewing the fountain show in a sleeveless summer dress, you may become somewhat perspiring. Upon entering Dubai Mall, however, you may wish you had long sleeves.