Overlooking Svínafellsjökull en route to the top.
In late July and August, the snow bridges covering the crevasses of the Icelandic glaciers are either unsafe to cross or completely gone. This depends on weather of course, but July and August is peak summer in Iceland and temperatures are high. Therefore, in those conditions, I do not go to Hvannadalshnúkur in late July and August.
However there is another option if you want to summit a high mountain that time of year. The neighbour peak of Hrútfjallstindar(1875m) is always in condition due to the nature of the crevasse fields there. It has similar characteristics including roped up glacier travel, even more spectacular view and varied terrain on the way.
It is equally difficult and long, 14-15 hours up and down. Please have a look at the equipment list to know what to bring, the preparation is the same as for Hvannadalshnúkur.