We present a method of estimating local heat transfer coefficients on the wall of a stirred vessel for highly viscous liquids fitted with various types of impellers using only numerical simulation. We analyze simultaneously specific flow and heat transfer behaviors in an unsteady state due to heating from the side wall of the vessel by finely dividing the analyzed region within a temperature boundary layer in the vicinity of the wall. The fluids used for analysis are a highly viscous Newtonian and a non-Newtonian pseudoplastic liquid. The impellers used are a six-blade paddle, a double-helical ribbon and an anchor type. We clarify the dynamic changes of the Nusselt number distribution along the vessel height direction from the beginning of heating to the pseudo-steady state, as follows: The distributions are rather flat and at high values just after the beginning of the heating. Subsequently, the values decrease as the temperature boundary layer develops. Further, the maxima of the values grow at the points of the vessel wall where the discharge flows from the impellers impinge. We also clarify that there is no striking difference in flow and heat transfer behaviors, except for the apparent viscosity distribution around the impellers, for each impeller vessel regardless of whether it is pseudoplastic or Newtonian, provided that both, the initial Red and Pr number are set to be identical for the two liquids. We ascertaine the reliability of the simulated estimates by verifying them with experimental results from a multi-point, real-time temperature measuring system which we have developed.