Turbine blade cooling has been a topic of significant interest, as increasing turbine entry temperatures result in higher cooling requirements. The present numerical method divides the blade into a finite number of elements in the span and peripheral directions and solves the heat transfer fundamental equations for convection and conduction in both directions. As inputs, the span and chord gas temperature and heat transfer coefficient distributions are required. The results include high resolution temperature prediction for the blade and coolant, at all span and chord positions. The advantages of the method include the capturing of blade temperature variation in all directions, while considering the thermal diffusion due to conduction. Mach number effects to the resulted blade and coolant temperature are highlighted, as local distribution of the gas static temperature can have a dominant role. The effect of averaging the input parameters to the predicted blade temperature is discussed and finally, different values for the material conductivity are simulated and the results are analysed.