A person (always male) too horny to bother using their brain. With their entire consciousness focused on sex, they usually don't bother to think about anything else. Especially what might happen or what is happening at that moment. Because they have sex so often, either with themselves or an actual partner, their dick is always smoking. Hence the term.
If Chris was watchin the road instead of gettin his umpteenth blowjob of the day, the stupid dick smoke woulda missed that tree.