  In this sequel to [1], we take up a second approach in bending the
Bruhat-Tits tree. Inspired by the BTZ black hole connection, we demonstrate
that one can transplant it to the Bruhat-Tits tree, at the cost of defining a
novel "exponential function" on the p-adic numbers that is hinted by the BT
tree.
  We demonstrate that the PGL$(2,Q_p)$ Wilson lines [2] evaluated on this
analogue BTZ connection is indeed consistent with correlation functions of a
CFT at finite temperatures. We demonstrate that these results match up with the
tensor network reconstruction of the p-adic AdS/CFT with a different cutoff
surface at the asymptotic boundary, and give explicit coordinate
transformations that relate the analogue p-adic BTZ background and the "pure"
Bruhat-Tits tree background. This is an interesting demonstration that despite
the purported lack of descendents in p-adic CFTs, there exists non-trivial
local Weyl transformations in the CFT corresponding to diffeomorphism in the
Bruhat-Tits tree.
