Technologies for managing Function-as-a-Service function requests based on thermal and power awareness include an edge entity device having a circuitry to receive, from an edge device, a request to execute a function in an edge network environment having a plurality of edge entities. The circuitry is also to evaluate thermal and power criteria associated with the request and determine, as a function of a predicted thermal output over a specified time period relative to thermal and power criteria, whether to execute the function. In response to a determination by the circuitry to not execute the function, the circuitry is to select an edge entity of a plurality of edge entities that is able to satisfy the thermal and power criteria. The circuitry is further to forward the request to the selected edge entity.