Transformer-based in-context learning (ICL) has demonstrated remarkable ability to perform regression tasks by conditioning on demonstration examples within a single forward pass, without parameter updates. While ICL predictions improve with more demonstrations, quantifying the uncertainty of these predictions with formal coverage guarantees remains an open challenge. In this work, we conduct a systematic empirical study of conditional conformal prediction methods— specifically CondConf and its computationally efficient variant SpeedCP—applied to ICL regression across multiple experimental axes. We investigate how model architecture (width, depth, and standard presets), task complexity (linear, quadratic, neural network, and decision tree regression), signal-to-noise ratio, and input dimensionality jointly influence both point prediction quality and the resulting conformal prediction intervals. Across 44 experimental configurations encompassing 12 architectures (S13–S24), 16 task–noise combinations (S52–S67), and 16 dimensionality configurations (S69–S84, 4 tasks × 4 dimensions), we find that SpeedCP maintains empirical coverage consistently near the nominal 95% level (93.1%–96.1%). However, the efficiency of conformal intervals—measured by average width—varies dramatically: from a 84% width reduction over the ICL trajectory for large-capacity models on low-noise linear tasks, to essentially no improvement for under-capacity models or high-noise regimes where irreducible noise dominates. At high input dimensions (d = 100), interval widths increase sharply despite separately training each model for its target dimensionality. These findings provide practical guidance for deploying conformal prediction in ICL systems and highlight the intimate coupling between model capacity, task learnability, and uncertainty quantification quality.