  The response of an integrable QFT under variation of the Unruh temperature
has recently been shown to be computable from an S-matrix preserving
(`replica') deformation of the form factor approach. We show that
replica-deformed form factors of the SU(2)-invariant Thirring model can be
found among the solutions of the rational $sl_2$-type quantum
Knizhnik-Zamolodchikov equation at generic level. We show that modulo conserved
charge solutions the deformed form factors are in one-to-one correspondence to
the ones at level zero and use this to conjecture the deformed form factors of
the Noether current in our model.
