Did you flush and bleed radiator before this happened?
If you left any air in the radiator, it will get pushed in the steam and when it goes past the temp sensor, it will show an overheat. But I cannot explain why heat comes out the vents with heat off.
If coolant is low you most likely have a leak somewhere, best to find and fix it before it overheats and crack the engine. Run engine hot then idle and shine a bright light into engine bay. Any leak or steam will be easy to find.
Cooling and overheating engine is the most serious problem for cars.