Hi, I have exactly the same problem. I was going to contact the support today and just wanted to check here first if I am really the only one with this problem. I'm glad I'm not.
I received my case (Turquoise) last week and when I put it on, the phone instantly rebooted. It took about half an hour until all apps where checked. The phone also got very hot.
I also have the feeling that apps were opened when the new case was on - even when I did not touch the phone at all. I tried to find out if one of the buttons was causing the problem and removed one by one. I also tried a battery reset several times. But when my phone is in the regular case everything is fine. As soon as I put the new slim case one, the phone behaves very strange. It gets hot, it reboots, it doesn't work properly.
I came tot the conclusion that the case must be a bit too tight.