Abstract: I will study the asymptotic behavior of a class of quantum refrigerators consisting of a parametrically driven network of oscillators which is coupled with an arbitrary number of thermal reservoirs. I will describe the fundamental process that enforces the validity of the third law of thermodynamics for this type of systems. This process, which prevents us from cooling a cold reservoir below a certain (non universal) temperature, consists of the non resonant creation of excitations pairs in the reservoirs and it is closely related with the dynamical Casimir effect. I will show that the results can be applied  to understand, in a simple way, the fundamental limits for laser cooling of a single oscillator.