Eu não acho que você possa recuperar uma sessão de navegação privada.
All session data is kept in memory during PB mode and nothing is stored in the Firefox profile folder. The disk cache is disabled as well and only the memory cache is used, so you can't find any data there as well. That is the risk when running in PB mode and you run into problems like a hang or crash that you can't recover from this and lose all data.
Fonte: link