Well, I said it too fast.
The infinite loop regarding the transferring of the ContactList to the car is no longer there.
However, the battery drain issue is still there. I left the house with a fully charged phone and within 3 hours, it was down to 1/2 tank again.
Took it to Apple Store and met with Genius Bar. I set up an appointment online but still had to wait more than 30 mins after check-in. 😟
Anyway Genius Bar ran hardware diagnostics and nothing was wrong. Bluetooth interface was tested using a keyboard and it seems to work fine.
So, he suggested wiping out the whole phone and start from scratch, like it is a new phone. He thinks it was software related.
We'll see if the battery drain issue goes away... also, while the phone was in my pocket, it was starting to burn my thigh because of the heat.