Deep Learning (DL) frameworks such as PyTorch and TensorFlow include runtime infrastructures responsible for executing trained models on target hardware, managing memory, data transfers, and multi-accelerator execution, if applicable. Additionally, it is a common practice to deploy pre-trained models on environments distinct from their native development settings. This led to the introduction of interchange formats such as ONNX, which includes its runtime infrastructure, and ONNX Runtime, which work as standard formats that can be used across diverse DL frameworks and languages. Even though these runtime infrastructures have a great impact on inference performance, no previous paper has investigated their energy efficiency. In this study, we monitor the energy consumption and inference time in the runtime infrastructures of three well-known DL frameworks as well as ONNX, using three various DL models. To have nuance in our investigation, we also examine the impact of using different execution providers. We find out that the performance and energy efficiency of DL are difficult to predict. One framework, MXNet, outperforms both PyTorch and TensorFlow for the computer vision models using batch size 1, due to efficient GPU usage and thus low CPU usage. However, batch size 64 makes PyTorch and MXNet practically indistinguishable, while TensorFlow is outperformed consistently. For BERT, PyTorch exhibits the best performance. Converting the models to ONNX usually yields significant performance improvements but the ONNX converted ResNet model with batch size 64 consumes approximately 10% more energy and time than the original PyTorch model.