Probably not great to have a car coming and going, my big girls who are now 9 months old still hate it when we pull in and out of the driveway and I'm convinced they think the school bus is eating my daughter!
As for heat, you have a few choices. You can make a heat cave:
https://www.backyardchickens.com/th...d-in-the-brooder-picture-heavy-update.956958/
Or you can do a heat emitting pad that only emits heat when they come in contact with it. I think this is better for older chicks going into the coop than newborns, though:
https://www.amazon.com/dp/B01LX9K1JI/?tag=backy-20
I know some use reptile heater bulbs which are different from standard heat lamps. Also, our babies were in a plastic tote and we used a heat lamp (125 watts) with no issues and just kept raising the height until taking it away. There is no chance, short of an electrical or wiring issue, that it ever got hot enough to melt the tub or burn cardboard.
Best of luck with whatever you choose and enjoy those babies!!!
ETA- If (well, who am I kidding...WHEN) I get baby chicks again I'll be doing the heat cave. It just seems the easiest, safest choice overall and no issue with the light being on all the time and them having to adjust to darkness when they are ready to go into the coop. That's just me, though. My chicks were brats about the dark those first few days without that constant red glow!