1998 Ford Ranger heater core

In my son's truck there is a strange smell in the cab and the windows fog up and a smoky mist comes into the cab through the air vents. The heat does not have to be on for the mist to come through the vents, but is a lot worse when it does get turned on and fills up the cab with the misty stuff. Regardless of the heater being on, after driving a short while when he turned the truck off and got out there was smoky stuff coming form under hood. The temp gauge never shows it was anything other then normal temp. I believe it is likely the heater core. Does that sound right or could it be something else?