ask his supervisor to regain control, or if he is UNsupervised, YOU need to become his supervisor. Point out the black streaks, and the mess he left behind, and say "I CANNOT have this continue. WE need to figure out a way to be cleaner about this. I know I have some suggestions on how to cut back on the dust, and dirt, but I would like to hear YOUR Plan on how you want to do this better? Do you have a tarp? did you bring covers for your shoes? can you vacuum more often? Can you hang a partition to protect my electronics from all of the dust up?

If he didnt bring supplies, lay bath room rugs or towels as a run way for him, and ask him to stick to it. You can provide a bed sheet to tack up to the doorway to prevent most of the dust from escaping to the other rooms. Give him an old bed sheet to use UNDER his cuttings. Remind him that altho this is a work space for him, its a LIVING space for you, and you would hate to present a reduced payment so that you can provide for the clean up that he has left behind.

If he is a smarty pants, CALL his boss, or the place you got the stove from. Ask them to provide assurance that it will be cleaned to YOUR satisfaction, or they will pay for the pro clean up after.