Methods and apparatus are disclosed to determine material parameters of a turbine rotor. An example apparatus includes a rotor geometry determiner to determine a geometry of the rotor, a node radius calculator to calculate radial node locations of radial nodes including a first radial node, a thermocouple interface to record first temperature values over an interval, a first thermal stress calculator to calculate first thermal stress values at one or more of the radial nodes over the interval, a node temperature calculator to calculate second temperature values at respective internal nodes of the first radial node, a reference value lookup to lookup first material parameter information, a second thermal stress calculator to determine second thermal stress values, a thermal stress comparator to calculate a difference between the thermal stress values, and, in response to the difference not satisfying a threshold, a material parameter adjuster to determine material parameters.