In reply to Dylan Driscoll:
Mid June to September, October if you are lucky.
Hochkönig is almost 3k m high, the higher elevations will be snowed under for quite a while. This can be especially tricky during descent via the Birgkar, where you may even want crampons and/or an axe until rather late in the season.
No good in thundery weather in July /August either, you don´t want to be caught on Austria´s longest lightning rod.
CB
