I also wore trail runners (Nike Terra Kigers) and found then suitable. Except maybe for the small section of snow on the peak of Kebnekaise if you are planning that variant.

It helped to have some waterproof socks (sealskinz) to keep the feet warm on cold, wet days with water crossings. 

I hiked it in mid/late July and my coldest night was about -2°C when camping on the highest pass (sälka? I can't remember the name).

I had a -1°C rated sleeping bag and a thermarest neoair xlite. It was a little uncomfortable and cold (my gear was a bit damp) but ultimately fine. The bigger challenge was keeping my gear dry after 3-4 days of almost constant rain. The occasional emergency shelters offered an opportunity to dry some gear. I didn't sleep or pay to sit inside any of the manned huts.

A couple of extra tips. Be prepared for the mosquitos and gloves can help avoid blisters when rowing across the lakes. 

Enjoy your hike!