Dedicated to the memory of Moshé Flato 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 replicadeformed form factors of the SU(2)-invariant Thirring model can be found among the solutions of the rational sl2-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 The form factor approach to massive integrable quantum field theories (QFTs) [9, 20] provides a powerful tool to compute exact matrix elements of local operators from the knowledge of the (factorized) S-matrix. To be precise, a form factor in this context is the matrix element of some local operator between the physical vacuum and a multi-particle