  We develop a time dependent random matrix theory describing the influence of
a time-dependent perturbation on mesoscopic conductance fluctuations in open
quantum dots. The effect of external field is taken into account to all orders
of perturbation theory, and our results are applicable to both weak and strong
fields. We obtain temperature and magnetic field dependences of conductance
fluctuations. The amplitude of conductance fluctuations is determined by
electron temperature in the leads rather than by the width of electron
distribution function in the dot. The asymmetry of conductance with respect to
inversion of applied magnetic field is the main feature allowing to distinguish
the effect of direct suppression of quantum interference from the simple
heating if the frequency of external radiation is larger than the temperature
of the leads $\hbar\omega \gg T$.
