Yes a/c is everywhere but unless you want an indoors holiday I would say don't bother unless it's June or never. Even in the evening it can be so hot and humid that being outside is very uncomfortable. June won't be too bad by Dubai standards.
Dubai in Summer (June – August)
Temperature: The air temperature during the season of summer fluctuates between 33°C and 42°C. Weather: The sun lets loose on Dubai during summer. Wave after wave of shimmering heat floods the city for 12 hours in the day. The temperature can skyrocket to the early forties, and sometimes go further to the fifties. The humidity and heat continue to escalate during these months. Sandstorms whip their way into the city, making it difficult to move around. Significance: With temperatures like these, most of the outdoor activities and festivals are restricted. However, the city doesn’t shut down entirely during this season. The Dubai Summer Surprises festival is spread over 10 fun weeks, with a theme assigned across the weeks. Everything from food, to art to nature is celebrated. Why you should visit now: Although the city is directly in eye of the sun during these months, Dubai’s interiors are air-conditioned and chilly, allowing you to stay comfortably inside during these months. Hotels offer great deals on both food and accommodation. What to know before the visit: Despite the heat, Dubai’s nightlife remains as vibrant as ever. Indulge in retail therapy, as the chilled malls are the best place to spend the summer day. Sandstorm season will also restrict your movements outside, so don’t plan any activities around the city unless it is vital. Tips: Hydration is key during this season. Make sure you’re drinking at least 2-3 litres a day and eat light meals – feeling full during the heat is uncomfortable, to say the least. Dress lightly and carry antiperspirant with you. Above all, try to keep all your trip activities indoor. The exception to this would be a desert safari but do check the weather in advance before you book.
The best time to visit Dubai is during the winter months, from November to April. Whether it’s the malls, the Burj Khalifa, the state-of-the-art venues, the plethora of activities, adventures and experiences and the overall entertainment provided.. January and February see heavy tourist traffic because of the Dubai Shopping Festival.