We consider the problem of area coverage for robot teams operating under resource constraints, while modeling spatio-temporal environmental phenomena. The aim of the mobile robot team is to avoid exhaustive search and only visit the most important locations that can improve the prediction accuracy of a spatio-temporal model. We use a Gaussian Process (GP) to model spatially varying and temporally evolving dynamics of the target phenomenon. Each robot of the team is allocated a dedicated search area wherein the robot autonomously optimizes its prediction accuracy. We present this as a Decentralized Computation and Centralized Data Fusion approach wherein the trajectory sampled by the robot is generated using our proposed Resource-Constrained Decentralized Active Sensing (RC-DAS). Since each robot possesses its own independent prediction model, at the end of robot's mission time, we fuse all the prediction models from all robots to have a global model of the spatio-temporal phenomenon. Previously, all robots and GPs needed to be synchronized, such that the GPs can be jointly trained. However, doing so defeats the purpose of a fully decentralized mobile robot team. Thus, we allow the robots to independently gather new measurements and update their model parameters irrespective of other members of the team. To evaluate the performance of our model, we compare the trajectory traced by the robot using active and passive (e.g., nearest neighbor selection) sensing. We compare the performance and cost incurred by a resource constrained optimization with the unconstrained entropy maximization version.