Summary: The heating of a compact dispersive target by a pulsed, plane microwave is modeled and studied herein. The dispersive character of the medium is described by a Debye model, and the conductive nature is modeled by an ionic conductivity. The electrical and thermal parmeters are allowed to depend upon temperature, which gives rise to a highly nonlinear initial boundary value problem. The governing equations are averaged in the limit as \(\omega T_ H\to\infty\), where \(T_ H\) is a characteristic time at which heat diffuses in the target and \(\omega\) is the microwave carrier frequency. A two-step algorithm is proposed for the numerical solution of these equations. When convection is weak, the algorithm converges very slowly. However, this problem is overcome by averaging the equations in the limit \(T_ H/T_ B\to 0\), where \(T_ B\) is a characteristic time describing energy loss by convection. This averaging yields a new theory from which a considerable amount of information can be deduced. Specifically, the temperature is spatially uniform in the target and evolves in time according to a first-order ordinary differential equation. The nonlinearity in this equation is a functional of the electric field within the target. This equation is solved for a number of specific examples, and physical conclusions are drawn about certain heating processes. Finally, the problem of controlled heating is addressed where linear feedback is shown to be adequate in achieving a predetermined final temperature.