Methods and apparatus for reducing temperature overshoot

Methods and apparatus for reducing temperature overshoot in an engine, such as in a gas turbine aircraft engine, are described. In an exemplary embodiment, an unmeasured temperature to be regulated in an engine is determined by measuring a temperature in the engine wherein the measured temperature being related to the unmeasured temperature, determining a bias of the measured temperature wherein the bias being an amount estimated to be a difference between the measured temperature and a steady state measured temperature and adding the bias to the measured temperature to restore the relationship between measured and unmeasured temperature so that the unmeasured temperature may be properly regulated. The bias is determined using a heat transfer model.