Federated Learning (FL) represents the de-facto standard paradigm for enabling distributed learning over multiple clients in real-world scenarios. Despite the great strides reached in terms of accuracy and privacy awareness, the real adoption of FL in real-world scenarios, in particular in industrial deployment environments, is still an open thread. This is mainly due to privacy constraints and to the additional complexity stemming from the set of hyperparameters to tune when employing AI techniques on bandwidth-, computing-, and energy-constrained nodes. Motivated by these issues, we focus on scenarios where participating clients are characterised by highly heterogeneous computing capabilities and energy budgets proposing EneA-FL, an innovative scheme for serverless smart energy management. This novel approach dynamically adapts to optimise the training process while fostering seamless interaction between Internet of Things (IoT) devices and edge nodes. In particular, the proposed middleware provides a containerised software module that efficiently manages the interaction of each worker node with the central aggregator. By monitoring local energy budget, computational capabilities, and target accuracy, EneA-FL intelligently takes informed decisions about the inclusion of specific nodes in the subsequent training rounds, effectively balancing the tripartite trade-off between energy consumption, training time, and final accuracy. Finally, in a series of extensive experiments across diverse scenarios, our solution demonstrates impressive results, achieving between 30% and 60% lower energy consumption against popular client selection approaches available in the literature while being up to 3.5 times more efficient than standard FL solutions.