In reply to slawrence1001:
Talking to the warden is the way to go. The Sasc Fura hut is only partially wardened in June, so you´ll maybe have to persevere with trying to get through. The main hut doesn´t open fully until July, but there´s a winter room available which takes 4 people.
https://www.sascfura.ch/en/huette.html
PS: even if the warden says it´ll be ok, be wary and prepared to retreat if necessary. We found the chimney pitches high on the Cassin route to be the hardest, and that´s obviously where any ice is going to linger longest. We were once told by the Civetta hut warden at the start of the season that our planned route should be fine (we were the first that year); it wasn´t, and we had to bale out halfway up.
Post edited at 16:35