The somatic gonad does not have adult stem cells (at least in vertebrates). The cells differentiate in the embryo and just stay differentiated. Nothing really needs to be inherited.
Epigenetics is not "how the genome is read" in any meaningful way. Epigenetics is more like encoding tone of voice transcription factors ought to use when they read the genome. Should they whisper or shout? Epigenetics does not do the actual reading of the genome, or change the underlying data in the base sequence. There are not "various readings" of the genome, no matter what you think.
So you haven't read the paper then. Perhaps you also don't understand the difference between mediates and regulates. KDM6B does not regulate the response to temperature. Temperature regulates something (unknown) that regulates KDM6B, which epigenetically regulates something else (in this case, DMRT1, a transcription factor) which regulates a bunch of other things (mostly unknown) that cause the gonadal soma to become testes or ovaries.
That epigenetics should play a bit part in some developmental process like this is essentially a trivial observation, and treating it as significant betrays a lack of understanding. All the genes in all the cells are wrapped around histones which are modified to make the underlying genes more or less active, all the time. So epigenetics a part of gene regulation, but it's hardly the most powerful or important one. It's like waxing poetic over the importance of uridine metabolism, because without uridine there is no RNA. It's true, but in a totally boring way.
As far as transgenerational epigenetics goes, essentially all of the literature in mammals is missing the key controls to rule out regular genetics. You should regard everything you read about it with extreme skepticism. It's a hot field with a lot of hype and pretty lax standards.