"Hot Jupiters" around red giants

What happens when a star becomes a giant and temperatures increase on orbiting gas giant planets? Possibilities of carbon-rich atmospheres from accretion of solar wind, but different wind patterns to tidally-locked hot Jupiters.

Jupiter will become a hot Jupiter: Consequences of Post-Main-Sequence Stellar Evolution on Gas Giant Planets

Would be interesting to simulate what happens after the peak temp to the moons of this new hot planets. Especially to Europa and Titan

There's actually a paper that talks about the outward migration of our solar system's habitable zone once our sun becomes a red giant. Interestingly enough, the paper suggests that the HZ will move out to Triton and beyond, possibly making Triton, Pluto-Charon, and Kuiper Belt Objects habitable environments.

The paper is "Delayed gratification habitable zones: when deep outer solar system regions become balmy during post-main sequence stellar evolution" by S. Alan Stern

Unfortunately , the article is not freely avaiable , only the abstract in pubmed.

How long would be this DGHZ in place ? some tens of milions of years or so? I don't think that would make for a viable evolutionary enviroment. Not even seeded from the inner planets eyecta.