White smoke is one thing, steam is another, particles floating another, dust another, rats nest cotton another, garbage and plant matter from the "air intake areas" is another. Be sure which it is. The only thing that can come out (if no leaks) is something on the "outside" of unit as you have said. Best idea is take it out, run the fan for a baseline look then take apart, inspect, clean, assemble and run the fan on the bench again. The sheet metal plenums could have rust, corrosion, dirt, scale, nest, debris that gets re-stirred up on each start up. That's if it's not actual smoke from the switch, fan motor or wiring. When you say coils it makes me think of electric heater, this has a heater core right? Anyway it all comes out very easily. Take the glove box off first. When someone connects the hoses together in the engine bay it means the unit was leaking into the cab. So be sure that it's not dripping, misting or seeping and is undetected by you.
