It’s fairly hot in Dubai so wearing light clothing is a good idea, but be mindful of the cultural sensitivities to "skimpy" clothing for women. It’s a very modern city, so wear what you would consider appropriate if you were walking around your own city. (Unless you live on a deserted island and only wear bikini bottoms!)
I always err on the side of caution, so recommend smart casual and ditch the tank tops. Dress shorts are ok, and steer clear of the belts disguised as shorts. about 6 years ago
You can definitely wear shorts and t-shirts/tank tops on the beach etc, but if you are in the malls or restaurants, then you are going to want to cover up as the AC will be set to "very cold" and you will freeze!
For modesty, its advisable for women to not wear skimpy clothing - short skirts/dresses/shorts, very tiny t-shirts, spaghetti tops etc. It will be tolerated - to a degree - but it will also bring a lot of unwanted stares, so unless you are on the beach or around the pool, a bit more would be preferable.
June will be hot, hot, hot. You wont be walking anywhere but you will be taking lots of taxis or the public bus. Bear this in mind. about 6 years ago
It could already reach up to 40C in June, so make sure you wear your sunscreen every 4 hours if you're planning to go outdoors. I think tank tops and shorts are reasonable but not too skimpy if you do not want to be stared at by men of all ages, and conservative Arabic women as well. about 6 years ago