Mobile robots in unknown cluttered environments with irregularly shaped obstacles often face sensing, energy, and communication challenges which directly affect their ability to explore these environments. In this paper, we introduce a novel deep learning method, Confidence-Aware Contrastive Conditional Consistency Model (4CNet), for mobile robot map prediction during resource-limited exploration in multi-robot environments. 4CNet uniquely incorporates: 1) a conditional consistency model for map prediction in irregularly shaped unknown regions, 2) a contrastive map-trajectory pretraining framework for a trajectory encoder that extracts spatial information from the trajectories of nearby robots during map prediction, and 3) a confidence network to measure the uncertainty of map prediction for effective exploration under resource constraints. We incorporate 4CNet within our proposed robot exploration with map prediction architecture, 4CNet-E. We then conduct extensive comparison studies with 4CNet-E and state-of-the-art heuristic and learning methods to investigate both map prediction and exploration performance in environments consisting of uneven terrain and irregularly shaped obstacles. Results showed that 4CNet-E obtained statistically significant higher prediction accuracy and area coverage with varying environment sizes, number of robots, energy budgets, and communication limitations. Real-world mobile robot experiments were performed and validated the feasibility and generalizability of 4CNet-E for mobile robot map prediction and exploration.