Repeated thermal optimization must enforce local temperature limits while solving linear systems whose unknowns change as the constraints activate and release. Zero-extension transfer, which carries correction vectors from one inactive set to the next, assigns zero to the degrees of freedom that a constraint has just released. We construct a spectral reference on the full state domain before optimization and restrict it directly to the current inactive set at each update, so the coarse correction receives reference entries at every released degree of freedom. Spatial and space--time constructions cover steady and transient conjugate heat transfer with prescribed fluid velocity, and a restriction-residual identity yields alignment and deflated-convergence bounds under stated rank and spectral-separation assumptions. In the primary comparisons on body-fitted transformer and bore-in-block models, the resulting reference deflation reduces the median complete optimization time relative to the tested iterative alternatives on the same graphics processor. Complete time includes reference construction. Matched transfer experiments connect the improvement to the reference information retained at released constraints. The lower cost persists on refined Cartesian and bore-in-block meshes, on space--time trajectories and over sequences with changing loads and query order; the margin narrows, and eventually reverses, as a trajectory gains time slabs at a fixed horizon. Full-domain reference retention thus supports repeated evaluation of temperature-constrained heat inputs in engineering thermal models.

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