Regarding this, my advice is to spend a measly amount on your nearest seamstress and have her sew you a cover. Yes, really.
(not being sexist btw, they're usually females, no offense was meant)
I have two kinds of covers; one is made from the same waterproof material jacket hoods are made of (slightly checkered, slightly glossy if that helps?), as it also happens to be extremely good at dust proofing. It's an ugly big square (has to fit even the Sigma entire) that when 'fitted' extends almost as far down as the desk's surface because dust and static combined don't need gravity to cause damage; it must be a full cover. Looks ugly though, yes.
The other is from the kind of semi-elastic (and always black) glossy thin fabric jogging pants are made of; reminds of NYLON though it isn't, as it has some linen in it as well. Also as tall.
Why two?
The latter for long term storage. Takes less space than the former and still covers your headphone entirely. But being of a much thinner material, it's also harder to dust (say with a Swiffer) because you'll move it and the headphones inside and harder to handle, as some care's required so that you don't bump/hit the headphone, especially when taking it off. But excellent due to its fabric for longterm storage.
The former for the one pair of headphones residing on your desk or right next to it, ie the ones you use every day. Being thicker and heavier, it's easier to take on and off without hassle (ie extending your hand too much), easier to 'sit' over them (being thicker means it also doesn't lose its shape, so this will remain as easy throughout the years) and harder to budge (say from a draft while having the window open). It's also impossible to get sunrays through it.
No offense to my favourite company, but their inhouse cover is a joke.
Cost me today's equivalent of 20 euros for the good one and 15 euros for each of the jacket-like ones (excuse my English..)? Worthy an investment and after 40ish years without the slightest issue on any of my phones, i think i'm entitled to attest as to their effectiveness.
Said it elsewhere, treat them as what they are; precision instruments. You don't just leave them hanging around
(inferring from the poster's comments above, i find it shocking they had them in a place directly hit by sunrays; 101 here. Again, no offense meant)