One of the most interesting directions in theoretical high-energy and condensed matter physics is understanding dynamical properties of collective states of quantum field theories. The most elementary tool in this quest are retarded equilibrium correlators governing the linear response theory. In this article we examine tensor networks as a way of determining them in a fully ab initio way in a class of (1+1)-dimensional quantum field theories arising as infra-red descriptions of quantum Ising chains. We show that, complemented with signal analysis using the Prony method, tensor network calculations for intermediate times provide a powerful way to explore the structure of singularities of the correlator in the complex frequency plane and to make predictions about the thermal response to perturbations in a class of non-integrable interacting quantum field theories.