Since warmer temperature makes it easier for the bubbles to escape, your drink will go from bubbly to flat much faster than it would if your tonic water were cool.
Gin and tonics are stirred to bring all the components together, but over-stirring them will release more of the trapped carbon dioxide gasses, resulting in a flatter drink.
So, unlike some other cocktails, a gin and tonic can't rely on vigorous stirring to let the ice cool down the drink, which is another reason to use cool tonic water.
If you don’t have cold tonic water, cool it quickly by wrapping the tonic bottle in a damp washcloth before putting it in the freezer — or chill the cocktail glass instead.