Predicting the receiving sensitivity of an offset Gregorian reflector system antenna requires an accurate prediction of the antenna noise temperature. Calculating the antenna noise temperature is computationally intensive especially for the electrically larger reflector systems. Using the main reflector masking technique, which removes the main reflector from the calculation domain, considerably reduces the computation cost. For an electrically smaller reflector system, diffraction effects affect the accuracy of this technique. Recently an improvement to the technique was proposed that introduces diffraction compensation correction factors. In this paper we introduce new compensation factor and interpolation techniques that improve the accuracy of the approximated antenna noise temperature calculation. The techniques are applied to several offset Gregorian reflector systems similar to those considered for the Square Kilometre Array, with various feeds and the accuracy in terms of receiving sensitivity is evaluated. The techniques can reduce the prediction error of the receiving sensitivity for frequency-invariant feeds to fractions of a percent, while maintaining a significant speed-up over direct calculations.