Time-series forecasting is critical for many real-world applications. Recent advances in time-series foundation models have substantially improved forecasting performance across diverse domains. However, most time-series foundation models remain deterministic and produce only point estimates without model confidence quantification, risking costly errors when faced with previously unseen data distributions. So called, selective forecasting mitigates this risk by enabling forecasting models to abstain from low-confidence predictions, trading coverage for improved reliability. In this paper, we introduce the Fine-tunable Time-Energy Model for time-series foundation models (FiTEM), a selective forecasting framework that extends pre-trained time-series foundation models, enabling selective forecasting. FiTEM appends a lightweight decoder to a pre-trained time-series foundation model and trains it via self-supervised learning during few-shot fine-tuning to produce confidence scores for each forecast and use those to reject low-confidence forecasts. FiTEM builds on state-of-the-art selective forecasting techniques requiring only a small amount of labeled target data and is trained as part of few-shot fine-tuning of a pre-trained time-series foundation model. We evaluate FiTEM on several time-series forecasting benchmark datasets unused during base model training in two modes: zero-shot, where FiTEM components are trained on limited target data without updating the parameters of the pre-trained foundation model, and few-shot, where the pre-trained model is few-shot fine-tuned on a small fraction of target data before FiTEM components are trained on the same data. Experiments show that FiTEM reduces forecasting error by up to \(56.4\%\) at low target coverage and up to \(35.4\%\) for target coverage of \(50\%\) and above.