Chosen Solution

During the startup process my MacBook freezes (start chime comes up and booting begins). Some seconds later it will shut off. When I try to restart the MacBook it turns off immediately. I suppose, that it overheats though the fan is running slowly. Does anyone know how to check the temperatures and/or the thermal sensors? Or maybe there’s some other problem? Please give me a hint.

It doesn’t have time to overheat. Try resetting the SMC: http://support.apple.com/kb/HT3964 then zap the PRAM: http://support.apple.com/kb/ht1379 Let us know of anything else it may be doing after you try these fixes.