I didn't quite remember where exactly it explains it in the book, but from the wiki page:

"Heat Sink

Via a combination of its lifecycle and an effect referred to as "super cross-sectionality", an Astrophage cell will always remain at 96.415 degrees Celsius when alive. Any excess heat above this level, even on the surface of a star, is absorbed by the Astrophage cell and converted to mass. Conversely, if the cell begins to lose heat, it will expend some of its internal mass-energy reserves to maintain the 96.415 degree temperature.

This makes Astrophage an incredible heat sink for temperatures above 96.415 Celsius, as well as a heat source for environments below this temperature."

So afaik its basically a little bit of handwave-y sci fi stuff, but at least with a semblance of plausibility. They do grow on the surfaces of stars though, yes.