Lots of factors play into the wad fouling. Obviously..barrel temperature, but there are other factors that play into it like what brand of wads are used and what the ambient temperature is.
Hunting dove in Argentina can have round counts above 1200 for a single shotgun in a day. Certainly not typical for most hunting in the US, but some conservation goose (unlimited or at least a high bag limit) seasons when the temperature is still up can also cause it.
I won't even start with the competition guys who do trap, skeet, 5-stand, sporting clays...etc. I know college shooting teams like Virginia Tech shoot several hundred shots in just a couple of hours. Fouling happens and accuracy suffers.
Look at it this way, companies wouldn't go through the trouble of making a product to dissolve the plastic from shotgun wads if it wasn't an issue.