In this talk, I will consider random dynamical systems composed of Pomeau-Manneville type intermittent maps with varying parameters. Assuming that the driving system is ergodic, Dragičević, González-Tokman, and Sedro (2025) established that the associated equivariant family of absolutely continuous measures satisfies linear response, i.e. it is differentiable in a weak sense with respect to perturbations of the system. In a suitable range of parameters, the system satisfies a (fiberwise) quenched central limit theorem. I will discuss the differentiability of the variance in the limiting normal distribution, which is the subject of our recent joint work with Davor Dragičević (University of Rijeka).