The 370'roof isn't as prone to temperature as the 350 and I rarely hear of issues with the roof mechanism not shutting properly. Sounds like something may be faulty.
If you have only had the car 1 day I would be taking it back to the place you purchased it and get them to fix it, unless it was a private sale, otherwise I would take it to a specialist to get it investigated. Don't mess with the 370 roof, if anything gets it out of alignment you are in for big expensive problems.