Temporal relation classification (TRC) demands both accuracy and temporal consistency in event timeline extraction. Encoder-based models achieve high accuracy but introduce inconsistencies because they rely on pairwise classification, while LLMs leverage global context to generate temporal graphs, improving consistency at the cost of accuracy. We assess LLM prompting strategies for TRC and their effectiveness in assisting encoder models with cycle resolution. Results show that while LLMs improve consistency, they struggle with accuracy and do not outperform a simple confidence-based cycle resolution approach. Our code is publicly available at: https://github.com/MatufA/timeline-extraction.