Why does room-temperature water feel cold to your hand if it is coming from a bowl of warm water but the same room-temperature water feels warm to your hand if it is coming from a bowl of ice-cold water?

Because your body get use to the warm water so when you put it in room temperature water it makes it seem colder. the it the opposite when the ice cold water your body gets use to the cold water and when you put in room temperature water it is warmer to your hand.