This is apparently a common issue with the 350z and 370z. An in cabin air filter should help. Your 2010 may have come with one stock but my 2009 did not. I suggest trying one of the charcoal flters. I got the standard STP one and had ok results but I will get the charcoal one next time.
DIY:
DIY: Adding In-Cabin air filter to the 370Z