The purpose of this work is to understand the effect of an external environment on an adiabatic quench through a quantum critical point. By means of general scaling arguments we derive an expression for the density of excitations produced in the quench as a function of its velocity and of the temperature of the bath. Finally, we corroborate the scaling analysis by considering a one-dimensional quantum Ising model coupled to an Ohmic bath and analyzing it in terms of a set of kinetic equations derived at weak coupling.