Transaction fee prediction in Bitcoin's ecosystem represents a crucial challenge affecting both user costs and miner revenue optimization. This study presents a systematic evaluation of six predictive models for forecasting Bitcoin transaction fees across a 24-hour horizon (144 blocks): SARIMAX, Prophet, Time2Vec, Time2Vec with Attention, a Hybrid model combining SARIMAX with Gradient Boosting, and the Temporal Fusion Transformer (TFT). Our approach integrates comprehensive feature engineering spanning mempool metrics, network parameters, and historical fee patterns to capture the multifaceted dynamics of fee behavior. Through rigorous 5-fold cross-validation and independent testing, our analysis reveals that traditional statistical approaches outperform more complex deep learning architectures. The SARIMAX model achieves superior accuracy on the independent test set, while Prophet demonstrates strong performance during cross-validation. Notably, sophisticated deep learning models like Time2Vec and TFT show comparatively lower predictive power despite their architectural complexity. This performance disparity likely stems from the relatively constrained training dataset of 91 days, suggesting that deep learning models may achieve enhanced results with extended historical data. These findings offer significant practical implications for cryptocurrency stakeholders, providing empirically-validated guidance for fee-sensitive decision making while illuminating critical considerations in model selection based on data constraints. The study establishes a foundation for advanced fee prediction while highlighting the current advantages of traditional statistical methods in this domain.