The fog radio access network (Fog-RAN) has been considered a promising wireless access architecture to help shorten the communication delay and relieve the large data delivery burden over the backhaul links. However, limited by conventional inflexible communication design, Fog-RAN cannot be used in some complex communication scenarios. In this study, we focus on investigating a more intelligent Fog-RAN to assist the communication in a high-speed railway environment. Due to the train's continuously moving, the communication should be designed intelligently to adapt to channel variation. Specifically, we dynamically optimize the power allocation in the remote radio heads (RRHs) to minimize the total network power cost considering multiple quality-of-service (QoS) requirements and channel variation. The impact of caching on the power allocation is considered. The dynamic power optimization is analyzed to obtain a closed-form solution in certain cases. The inherent tradeoff among the total network cost, delay and delivery content size is further discussed. To evaluate the performance of the proposed dynamic power allocation, we present an invariant power allocation counterpart as a performance comparison benchmark. The result of our simulation reveals that dynamic power allocation can significantly outperform the invariant power allocation scheme, especially with a random caching strategy or limited caching resources at the RRHs.