Recently, physical layer (PHY) caching has been proposed to exploit the dynamic side information induced by caches at base stations (BSs) to support Coordinated Multi-Point (CoMP) and achieve huge degrees of freedom (DoF) gains. Due to the limited cache storage capacity, the performance of PHY caching depends heavily on the cache content placement algorithm. In existing algorithms, the cache content placement is adaptive to the long-term popularity distribution in an offline manner. We propose an online PHY caching framework which adapts the cache content placement to microscopic spatial and temporary popularity variations to fully exploit the benefits of PHY caching. Specifically, the joint optimization of online cache content placement and content delivery is formulated as a mixed-timescale drift minimization problem to increase the CoMP opportunity and reduce the cache content placement cost. We propose a low-complexity algorithm to obtain a throughput-optimal solution. Moreover, we provide a closed-form characterization of the maximum sum DoF in the stability region and study the impact of key system parameters on the stability region. Simulations show that the proposed online PHY caching framework achieves large gain over existing solutions.