Have you ever noticed a minor vibration that appears to go away in about five minutes of driving, only to appear the next morning? What you're experiencing is a phenomenon called flatspotting. The tire develops a "square" side because of the weight of the vehicle resting on the tire. Tires are more apt to flatspot during colder weather, therefore drivers in the Snowbelt will begin to notice this in the fall. Higher speed rated tires are more likely to flatspot because they use a cap of nylon or polyamide that's between the steel belts and tire tread to reinforce the tire so it can survive the high-speed test.
As the tire warms up it becomes "round" again, causing the vibration to go away. It's particularly annoying for drivers that have short commutes because their tires never get a chance to lose the vibration.
Flatspotting can occur on any vehicle but it's often masked so it's unnoticeable. Every once in awhile it can show up in new versions of an existing model. For example, when Acura launched the 2004 Acura TL, most TLs were equipped with the Bridgestone Turanza EL42 (not to be confused with the Turanza Serenity and its replacement the Turanza Serenity Plus) and many drivers experienced flatspotting on their vehicle.
How do you go about solving this issue? Many drivers experience much less or no flatspotting by switching to a tire that uses a polyamide cap instead of a nylon cap because nylon tends to have a memory effect.
If you're looking for tires that are more resistant to flatspotting, try to pick an option with a polyamide cap instead of nylon. Many manufacturers, such as Michelin have begun to use polyamide more.