No, it's a bit smelly when you first peel off the backing but once it's stuck on there's no smell at all, even when it heats up. I definitely wouldn't use it if it did, asphalt and petroleum smells in general give me a headache nowadays.
Give it time. Also wait for it to fall off the ceiling and onto the headliner. Hopefully you have a board not just the rods/cloth. I've had the pleasure of helping a friend remove this from a car he did when it hit 100 degree's out and it melted off of everything.
