Hi Mark.
I went to Iceland for two weeks in August several years ago. We toured the island with a small organised coach group visting the southwest, centre, and northeast of the island. We had absolutely no trouble with midges or any other insects at all and I'm sure you won't. It's too cold and windy for them really but do take plenty of warm clothes.
You will love Iceland and I wish I was going back. Its so peaceful and quiet and the people are so warm, friendly and pleasant. The landscape is breathtaking and the wildlife, volcanoes, glaciers and geothermal areas are stunning. I remember one viewpoint from where we could see more than 60 volcanoes! Although it is usually very windy and cold the air is so clean and fresh. You will also notice that everything smells of rotten eggs as the hot water is piped free straight from the ground and it is loaded with sulphur which gives the smell. Shops, people, houses and you will stink of sulphur but you don't notice it after about three days. Try the local foods too such as two-year old smoked salmon and raw, dried cod. They are surprisingly good.
Sorry to eulogise but I loved Iceland so much and you will too. You will never forget the country and the people. Have a great time.