My 930 barrel gets pretty toasty.No. To be honest, I have fired the shotgun a lot. Semi auto. Dumping out a lot of rounds in short order.
I have never gotten the barrel hot enough to burn you or hot enough to melt something. Or the handguard.
I have made my own heat shields for silencers though. They certainly can get hot enough to brand you. Shotguns though? I've never seen that happen.