We report system and algorithm developments that utilize a single mobile robot to simultaneously localize multiple unknown transient radio sources. Because of signal source anonymity, short transmission durations, and dynamic transmission patterns, the robot cannot treat the radio sources as continuous radio beacons. To deal with this challenging localization problem, we model the radio source behaviors using a novel spatiotemporal probability occupancy grid that captures transient characteristics of radio transmissions and tracks posterior probability distributions of radio sources. As a Monte Carlo method, a ridge walking motion planning algorithm is proposed to enable the robot to efficiently traverse the high-probability regions to accelerate the convergence of the posterior probability distribution. We also formally show that the time to find a radio source is insensitive to the number of radio sources, and hence, our algorithm has great scalability. We have implemented the algorithms and extensively tested them in comparison with two heuristic methods: a random walk and a fixed-route patrol. The localization time of our algorithms is consistently shorter than that of the two heuristic methods.