Quantum quench - a sadden change of system Hamiltonian - provides a rich and tractable framework to access dynamics of thermalization of a quantum isolated system. When the chnge of Hamiltonian is fast but not instantaneous (so called fast quenches) the dynamics often can be described in terms of the UV fixed point, thus leading to universal predictions. We employ conformal perturbation theory to calculate the behavior of various quantities (one and two point functions) during and after the quench. Furthermore, by calculating the energy fluctuations after the quench we argue that at late times the system will thermalize, provided it satisfies the Eigenstate Thermalization Hypothesis.