This is not really a help request, since I already figured how to circumvent the issue (I don’t know if I should instead post a bug report, please point me to the tracker if I should).
My laptop is a bit old and has a Nvidia optimus card. By default, the live-usb runs the discreet card all the time and therefore overheats to the point it just shutdowns. Disabling this card on the live system is not an option because it would require to install bumblebee and run the service, but you can’t unload the Nouveau driver to disable the card (AFAIK).
So far my solution has been to start the system with a nomodeset option (which gives a lesser screen resolution, which is not optimal).