The inherent thermal time constant and initial temperature jump appeared in using resistor type temperature sensors can be assessed by a fast convergent reading technique, that can be used to predict the final temperature reading at the beginning stage of temperature measuring process. The resistance changing rates within RTDs, proportional to a temperature changing rates, of the first few readings in the sensor and its followers are fed into a programmed microprocessor for numerical calculations, in order to get beforehand the time constant as well as the final temperature that normally does not change instantaneously in response to the step-function temperature change from the body in contact. The calculations will be able to forecast the would-be final reading in the foreseeable time frame, and thus can expedite the process and overcome the retardation in temperature measurement resulted from the slow progression of time-temperature history as time to reach thermodynamic equilibrium between sensor body and the heat conduction media is strongly affected by the thermal time constant and temperature jump.