Abstract
White Rabbit (WR) attains sub-nanosecond synchronisation by treating the fibre asymmetry coefficient as a one-time calibration constant, neglecting the thermo-optic dependence of the refractive index on temperature — an effect that grows with link length. We show that for a 150 km link, a fixed asymmetry coefficient introduces a picosecond-scale systematic one-way-delay bias under multi-degree path-averaged drift, scaling linearly with length. We reformulate the WR delay model with explicit temperature dependence, anchoring on the time-invariant-assumed fibre length, so the average fibre temperature drift can be estimated from standard PTP timestamps and folded into the control loop error signal without disturbing phase tracking; a constant-velocity Kalman filter then smooths timestamp noise and predicts the link delay between exchanges. Evaluated against published long-range WR configurations, the algorithm improves long-term time deviations at averaging times above 1000 s under a 5 K peak-to-peak diurnal swing, with the gain widening as the PTP exchange rate is lowered and the prediction step bridges longer gaps. In simulation, the same estimator also recovers an effective path-averaged fibre-temperature drift from timing data alone, suggesting a possible zero-added-hardware sensing by-product rather than a field-calibrated temperature-sensing claim. These results position long-range White Rabbit as a timing infrastructure for deterministic 6G continuum networks, where relaxed timing-message exchange can reduce control overhead while preserving long-term synchronisation stability.