The availability of cheap and easy-to-install sensors is bolstering the development of monitoring applications in IoT scenarios. Although there is a need for periodical measurements of the tracked signals to guarantee an accurate representation at the receiver, choosing an appropriate duration for the reporting window is not trivial. In fact, the energy restrictions of many devices and the interference caused by other users call for longer reporting windows. However, this causes a higher reconstruction error due to the lower sampling resolution, which may be unacceptable in some applications. We propose a probabilistic random channel access scheme for battery-powered devices which monitor time-correlated phenomena and report their measurements to a fusion center. Our goal is to minimize the energy consumption of the sensors, while guaranteeing that the error in the signal estimate at the receiver does not exceed a chosen threshold. We exploit Markov chains and stochastic geometry to characterize the interference caused by the other devices. The numerical evaluation proves that our scheme is scalable and may be used in highly dense scenarios, and that it outperforms other state-of-the-art approaches, which do not consider the impact of interference on both the energy consumption and the accuracy of data representation.