Sometimes there could be other reasons for this, faulty Simcard, faulty memory card or it can be some bad 3rd party app running in the background.
If you have installed a memory card, you could try a bit without it to see if that may be the cause, but as it is brand new, and if you haven done anything special to it, I would take it to a Nokia care point to get it checked.
Thank you for your replies. I have an 8 GB memory card in my phone, but it's older, I also used it on an LG phone, so I don't think that this is the problem. But let's exclude everything possible 
The problem with the Nokia Care centers is that...there aren't any!! I live in Germany in a big city and not even in bigger cities Nokia hasn't got any care centers. I looked on the nokia website and on Google, too. So this thing with the care center is a big, fat lie. Thanks, Nokia. I expected a little bit more when paying some hundred Euros on this mobile phone...
Anyway, some of these wierd shutdown behaviors seems to look like some of the issues faced with the N8. And if it is, a trip down to the Nokia care point would be the only solution, or take it back to the reseller/store/shop you bought it from and make them deal with it. If it has been some time, they would probably send it to a care point, so taking it self would might save some time. But if it's brand new, I would take it back to the store first and demand a new one. It might work out.
It could be those issues I stated in my first post, but if you have tried what suggested and it does not help, or you don't want to bother a Nokia care point might be the only solution.
. seems it is time to send it back 
Hello sir/madam,
I recently bought a new Nokia C6-00 phone on 1-12-2010 and ever since it keeps turning off by its own in various situations - no matter if the phone just lies on the table .The battery is full,even if the phone is not connected to any device.
sometimes when I lock the keyboard and put the phone elsewhere it switches off, without any warning. ...............The most annoying thing is that if I want to switch it on again, I have to take out the battery, wait a couple of seconds, then try turning it on again. Otherwise it won't work!..........and it usually hav the problem of hanging.....and sometimes when i lock my phone n when try to unlock it ,it sometime do nota unlock also......!!!! 
It stArted giving problem after 4-5 days of purchase, when i told abt this to the retailer[a retailer of Rajajipuram, Lucknow], he gave me the option of replacing it......
i hav been to nokia care 3-4 times but they always update the software and then after sometime it again starts giving the same problem.........and i also asked the nokia care to replace it with the new one bt they are ignoring my request.....................N NOW I WANT TO REPLACE IT BY HOOK OR CROOK!!!!!!
what should i do???????
i should case against nokia for not co-operating with its customers???????
Finland, china etc. Hardware parts, manufacturing process, quality controls are the same.
Unfortunately some phones has this issue which are probably related to malfunctioning hardware parts and has nothing to to with where the phones are made.
That finland phones are better is just an old rumour that has no root in the real life.
