Forced time-domain oscillations in a cavity filled with a temporally dispersive polar dielectric are studied. The cavity is bounded by a singly connected closed perfect electric conductor surface$S$of rather arbitrary shape. A given source pumps a signal of finite duration to the cavity. Hence, the principle of causality is involved in the formulation of the problem. The temporal cavity oscillations are obtained as a self-consistent solution to the system of Maxwell's equations and Debye equation supplemented with appropriate initial conditions . Analytical solution is obtained by using the evolutionary approach to electromagnetics proposed and implemented recently. Temporal oscillations of the cavity modes are studied. Obtained results are compared with the finite-difference time-domain solutions.