is the dock standing in an open area? make sure there's room behind it, that's where it draws in air.
that said, yes, the switch does get warm in some games, like BotW and probably yoshi too and that's perfectly normal.
warm and hot are rather subjective terms, so does it feel like a radiator? if you touch it for a couple seconds, would you say it's painfully hot?
the noise sounds questionable. i know you can hear the fan when you get close with your ear, but it shouldn't really be very notable when there's game sounds in the room.
does it sound weird? like, scratchy, clanky? is the air-flow constant?