Then I’ll quote and respond to your edited comment:
There is. It’s a bit of a pain and eats a lot of the precious flash space but it is doable. Some info on my tests here: ATTiny13a tempurature monitoring without additional components. (image host links don’t work anymore).
Unfortunately I don’t have that code left though, it was so long ago I did anything with the 13a and I’ve gone through multiple ATtiny’s since then (currently on the ATtiny 3217). I suggest you move on from that little 13a you too.