We employ holographic techniques to study quantum quenches at finite
temperature, where the quenches involve varying the coupling of the
boundary theory to a relevant operator with an arbitrary conformal
dimension. The evolution of the system is studied by evaluating the
expectation value of the quenched operator and the stress tensor
throughout the process. The time dependence of the new coupling is
characterized by a fixed timescale and the response of the observables
depends on the ratio of the this timescale to the initial temperature.
The observables exhibit universal scaling behaviours when the
transitions are either fast or slow, i.e., when this ratio is very small
or very large. For fast quenches, we uncover a universal scaling
behaviour in the response of the system, which depends only on the
conformal dimension of the quenched operator in the vicinity of the
ultraviolet fixed point of the theory.