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That will depend upon if the fumes get into the first floor or not. Personally, I think I would use something like several joss sticks & see if you can smell those on the first floor. I have used those bug bombs downstairs & not smelt anything upstairs & used others & they have stunk the whole house out.
I wouldn't risk it personally, if the vapor from those gets into your vents it can be carried throughout the house. I'd probably keep your T out of the house for a few days if you're going to bug bomb it.