[en] We present a general model of a quantum parametric oscillator heated by coupled fluctuating fields. Two kinds of external fields are considered: an external fluctuating driving force, and a noise in the basic frequency of the oscillator. The energy increase and the change in the square variances of position and momentum produced in such systems are calculated. As a particular example, we study the case of a Paul trap and the evolution of coherent and squeezed states under general conditions. The analysis is also extended to the evolution of superpositions of coherent states