1. An electronic clinical thermometer comprising: temperature detecting means for detecting temperature at a part of a body and for generating a first signal indicative of the detected temperature; storage means for sequentially storing the first signal; elapsed time measuring means for measuring time which has elapsed since start of measurement and for generating a second signal indicative of the measured elapsed time; first arithmetic means for reading the first signal, corresponding to a prescribed length of past time, out of said storage means to obtain a mean value during said length of past time, and for producing a third signal; second arithmetic means for obtaining a predicted value of a stable temperature from the second and third signals on the basis of a stable temperature prediction function in which measurement time is a variable, the function defining a temperature change up to final, stable temperature; first control means in response to which arithmetic operations are performed by said first and second arithmetic means at a predetermined period; display means for displaying the predicted value of stable temperature; and second control means responsive to said elapsed time measuring means for subjecting the first signal and third signal to a comparison at two successive points in time; wherein after said second control means determines that the second signal has exceeded a first prescribed elapsed time and that a difference exhibited by the third signal corresponding to two successive points in time no longer shows an increase outside a first prescribed range, the third signal corresponding to a present point in time is compared with the third signal at the preceding point in time and, when the first signal exhibits a decrease outside a second prescribed range, said second control means halts the operation of said first and second arithmetic means.