If you can plan a visit at short notice around the weather, the situation likely to produce the best flying conditions is a weak high pressure system, centred directly over the Alps or slightly to the northeast, with no fronts or troughs nearby. The less there is to see on the synoptic chart, the better! The pattern shown below is likely to bring hundreds of Swiss pilots to Fiesch in the summer, even on a weekday.
To minimise the risk of experiencing challenging conditions, it’s best to choose days when the weather is as quiet as possible: light winds (best between south and west), minimal air pressure gradients in all relevant axes, a dry airmass, and a steady rather than ballistic lapse rate without significant inversions. Approaching cold fronts and troughs are particularly dangerous, because of the rapid unpredictable changes in wind strength and direction which they can cause in these big mountains. I once encountered a sudden 50 km/hr ground level wind in the Goms, caused by a storm around Martigny, 100km to the west, which blasted a gust front from there all the way up the Rhône valley.
In the summer, unless the weather is obviously unflyable, you can usually expect to find a few local pilots around at the main landing field to help you to form an opinion about the day before committing yourself to the trip up the mountain to take-off. I have also always found the staff of both schools based in Fiesch to be exceptionally helpful towards visiting pilots asking for information about the conditions, and usually very forthcoming with advice. You should not assume that it is likely to be safe to fly all day simply from seeing others in the air, as they could be professional tandems, acro pilots getting in some practice, or the ignorant pushing their luck before conditions deteriorate and catch them out.
For specific details explaining how certain weather factors influence the flying conditions around Fiesch, see the pages under the Winds heading. You can find meteo sites to use for flight planning in the Looking ahead and On the day pages in the Links section.