This paper extends the paradigm of "mobile edge learning (MEL)" by designing an energy-aware optimal task allocation scheme for training a machine learning (ML) model in a semi-asynchronous manner across multiple learners connected via the resource-constrained wireless edge network. The tasks are allocated such that the local dataset size selected at each learner ensures completion within a given global delay constraint and a local maximum energy consumption limit. Hence, the designed method is heterogeneity aware (HA) because it offers a trade-off between resource consumption and MEL performance by directly relating the time and energy consumption to the heterogeneous communication/computational capabilities of learners. Because the resulting optimization is an NP-hard quadratically-constrained integer linear program (QCILP), a two-step suggest-and-improve (SAI) solution is proposed. The proposed HA semi-asynchronous (HA-Asyn) approach is compared against the HA synchronous (HA-Sync) scheme and the heterogeneity unaware (HU) synchronous/asynchronous (HU-Sync/Asyn) equal batch allocation schemes. Results from a system of 20 learners tested for various completion time and energy consumption constraints show that the proposed HA-Asyn method works better than the HU-Sync/Asyn approaches and can even provide gains of up-to 25% compared to the HA-Sync scheme.