Hi timyb,
Are there any panic logs posted on your phone? If so, they'll help pinpoint the cause of the restarts. There's an excellent write-up on them over on the Wiki pages.
[[iPhone Kernel Panics|iPhone Kernel Panics - iFixit|new_window=true]]
Instructions are include on how to locate the panic logs and a lot of information on how to interpret them. If you post the first page or so of any logs you find, we can take a look and see what we can do to help decode them.