The simple answer is No, you can not have a loaded firearm in your car unless you have a carry permit.
Unloaded doesn't just mean no ammo in the firearm either...
T.C.A. 39-17-1301(18) defines unloaded as "the rifle, shotgun or handgun does not have ammunition in the chamber, cylinder, clip or magazine, and no clip or magazine is in the immediate vicinity of the weapon."
Also the weapon can not be concealed on your person or the ammo in your immediate vicinity.
Defenses to unlawful possession or carrying of a weapon.
It is a defense to the application of § 39-17-1307 if the possession or carrying was:
T.C.A. 39-17-1308(a)(1) Of an unloaded rifle, shotgun or handgun not concealed on or about the person and the ammunition for the weapon was not in the immediate vicinity of the person or weapon;