Over time, direct sunlight is death, at least for the paint job, it will totally fade out all colours and mostly end up looking nothing like it once did.
Smoke would be really bad for the PF's, as it would start to get into the cloth and hence end up always smelling like smoke. Maybe not as bad for pure polystone, but still.
Dust isn't the best for any of it, it's not the actual dust, it's the oil in the dust (a lot of dust is in fact dead skin), so over time, the oil will react with the paint as well, and start to fade them.
So yes, behind glass is good (locked glass is even better, stops, pets, little figures or even mates, grabbing and breaking stuff), and even dusting is still a good idea once in a while. If not behind glass, then dusting often is a must.
Temperature or more the point humidity can had a impact on PF's more then anything. You can get mold on the cloth, so it will discolour and may even start to break down. Less of an issue with pure polystone, but even so, you don't want to cook or freeze them.