I searched all the forums and did not find a "hit" for a similar posting, so I wanted to post my experience so that hopefully somone else can learn from my experience and not repeat my mistake.
I bought a new Thule 968 2-bike capacity bike rack that mounts to the rear of my Ford Focus hatchback. I then put my Lemond Tourmalet on the outer mount. I used the supplied strap to hold the wheels steady to the bike rack frame and to pull the bike towards, but not touching, the rear bumper to minimize swinging. I successfully transported it several hours to my destination (Solvang California Double Century).
On the way home, I decided to mount the bike on the inner of the two mountings and again used the supplied strap to hold the wheels steady and to pull the bike towards (but not touching) the rear bumper.
I positioned the bike so that it was evenly speced with the back of the car, with the outside of the wheels being about even with the sides of the car.
When I unloaded the bike upon arriving home, I was dismayed to discover the the rear tire must have been directly behind the exhaust pipe, since the tire was melted, the tube flat, and the tire partially melted to the rim.
The lesson from the story is to either remove the tire on the exhaust pipe side or to position the bike in such a way that the rubber tire is not directly in line with the exhaust pipe.
I was disappointed that the rack installation instructions provided no caution to be on the lookout for this potential problem that did not even cross my mind.