Exploration of spatial processes, such as radioactivity or temperature is a fundamental task in many robotic applications. In the literature, robotic exploration is mainly carried out for applications where the environment is a priori known. However, for most real life applications this assumption often does not hold, specifically for disaster scenarios. In this paper, we propose a novel integrated strategy that allows a robot to explore a spatial process of interest in an unknown environment. To this end, we build upon two major blocks. First, we propose the use of GP to model the spatial process of interest, and process entropy to drive the exploration. Second, we employ registration algorithms for robot mapping and localization, and frontier-based exploration to explore the environment. However, map and process exploration can be conflicting goals. Our integrated strategy fuses the two aforementioned blocks through a trade-off between process and map exploration. We carry out extensive evaluations of our algorithm in simulated environments with respect to different baselines and environment setups using simulated GP data as a process at hand. Additionally, we perform experimental verification with a mobile holonomic robot exploring a simulated process in an unknown labyrinth environment. Demonstrated results show that our integrated strategy outperforms both frontier-based and GP entropy-driven exploration strategies.