I have been a mechanic for 35 years.
I have suggested to you, to get the car towed to the dealership.
Your observation of "smoking", and then lifting the hood is commended, but the dealer not requesting the vehicle to be towed is dumb on their part, especially for a vehicle under warranty.
A vehicle's cooling system is made up of many parts, some are more prone to failure.
To say what part has failed would be guessing, it could be a leaking or damaged hose, it could be a damaged radiator, it could be a thermostat, head gasket, cooling fan, or an electronic issue.
Driving the vehicle to a now overheated condition has probably hurt the engine.
I have given you a simple answer to a simple question.