Stochastic Timed Automata (STA) associate logical locations with continuous, generally distributed sojourn times. In this paper, we introduce Networks of Stochastic Timed Automata (NSTA), where the components interact with each other by message broadcasts. This results in an underlying stochastic process whose state is made of the vector of logical locations, the remaining sojourn times, and the value of clocks. We characterize this general state space Markov process through transient stochastic state classes that sample the state and the absolute age after each event. This provides an algorithmic approach to transient analysis of NSTA models, with fairly general termination conditions which we characterize with respect to structural properties of individual components that can be checked through straightforward algorithms.