As the demand for data privacy and low latency grows, edge computation carried out at edge data center nodes is believed to become increasingly important for future telecom applications. Providers must consider various factors, including power consumption, thermal dynamics, and the ability to maintain high-quality service, in addition to deployment and service orchestration. This paper presents a detailed description of two different prototype edge data centers designed to investigate the power performance and thermal dynamics of edge nodes under various applied services. The prototypes were developed and tested at the RISE ICE Datacenter research facility. We present the results of power flow experiments in which input current from the grid was limited while the computational load was maintained using the energy stored in batteries. We further discuss implications for placing edge data center nodes in locations with temporal power constraints and opportunities for participation in support services at the grid level.