The automatic detection of temporal relations among events has been mainly investigated with encoder-only models such as RoBERTa. Large Language Models (LLM) have recently shown promising performance in temporal reasoning tasks such as temporal question answering. Nevertheless, recent studies have tested the LLMs' performance in detecting temporal relations of closed-source models only, limiting the interpretability of those results. In this work, we investigate LLMs' performance and decision process in the Temporal Relation Classification task. First, we assess the performance of seven open and closed-sourced LLMs experimenting with in-context learning and lightweight fine-tuning approaches. Results show that LLMs with in-context learning significantly underperform smaller encoder-only models based on RoBERTa. Then, we delve into the possible reasons for this gap by applying explainable methods. The outcome suggests a limitation of LLMs in this task due to their autoregressive nature, which causes them to focus only on the last part of the sequence. Additionally, we evaluate the word embeddings of these two models to better understand their pre-training differences. The code and the fine-tuned models can be found respectively on GitHub.