Unsteady transonic flows induced by the heat released during condensation of water vapor near the throat of a converging-diverging nozzle have been observed by Wegener and Cagliostro (1973) among others. Unsteady transonic flows with heating may also arise in air blast circuit breakers and in various processes involving the flow of chemically reactive gases. A theory for such flows is developed. The flow is shown to be isentropic and irrotational to first order. Small disturbance potential equations are derived. The oscillatory flows observed by Wegener and Cagliostro are shown to fall in the slowly time varying regime. An exact solution of the slowly time varying equations is found for flow near the throat of a nozzle with uniformly distributed oscillatory Joule heating.