During drilling circulation, the wellbore temperature field changes in response to drilling-fluid rheology, borehole geometry, drillstring eccentricity, and cuttings concentration. Conventional wellbore temperature models use fixed heat-transfer parameters and therefore cannot accurately represent real-time heat-transfer conditions. To address this limitation, a transient temperature model was developed. Bottomhole annular-fluid temperatures generated by OLGA were used as synthetic observations for MHE calibration. An MHE-based calibration method was developed to estimate the equivalent heat-transfer correction factor. The temperature model was first benchmarked against the Kabir analytical model and the commercial simulator OLGA. The estimated correction factor was then used by the mechanistic model to update the wellbore temperature field. The results showed that, under different initial values of the correction factor and assumed measurement-noise standard deviations, the equivalent heat-transfer correction factor converged to a steady-state value of approximately 0.941. Additional sensitivity tests showed generally stable calibration performance under moderate parameter settings, whereas stronger observation noise reduced calibration stability and accuracy. Under varying operating conditions, the calibrated bottomhole temperature yielded a mean absolute error of 0.033–0.332 °C, representing a reduction of 45.97–98.73% relative to the corresponding uncalibrated results. When the observation delay was extended to 2400 s (d = 8), the MAE was still reduced by 26.50–68.20% across different operating stages. These numerical results show that the proposed method can use bottomhole temperature observations to dynamically compensate for equivalent heat-transfer model mismatch under the investigated simulation conditions. The method reduces model-prediction errors and improves bottomhole temperature prediction under the tested varying operating conditions. The proposed method has potential applications in wellbore temperature prediction and high-temperature risk assessment for deep-well drilling.