Deploying model predictive control (MPC) requires constructing or identifying a predictive model for each target system. Time-series foundation models (TSFMs) offer an attractive option thanks to strong zero-shot forecasting capabilities across systems. However, low forecast error does not guarantee that a TSFM captures the system's response to the alternative actions considered by the controller. We study this gap using residential heat-pump control as a test bed, measuring the agreement between predicted and ground-truth effects of control interventions. Importantly, we find that TSFMs can recover the system's input-response relationship when the context contains sufficient independent control excitation. Common fine-tuning pipelines and feature smoothing reduce, but do not eliminate, the need for in-context excitation. Our results indicate that current TSFMs used for predictive control require sufficiently informative control variation in the inference context. Initial closed-loop results show promise for shorter context windows.

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