No it's not... plugged in?
Black plugs are caused from over fuelling or loss of spark. It runs ok when it's cold so it must have a good spark. It's as if the ecu isn't being told the engine is hot and is pumping in fuel as it thinks it's still cold (choke).
Is I think it could be...
Air flow sensor, the car thinks lots of air is going in so it's compensating by stuffing loads of fuel through.
Ecu temp sensor, thinks its still cold so effectively it's keeping the choke open.
Crank shaft sensor, confusing the ecu and trying to compensate again with more feul.
Smokey exhaust is because of the over feulling and it's coking up and spitting it out the exhaust.
Is your temp gauge slightly different to where it normally sits?