A thermometer that rapidly predicts body temperature based on the temperature signals received from a temperature sensing probe when it comes into contact with the body. The logarithms of the differences between the temperature signals in a selected time frame are determined. A line is fit through the logarithms and the slope of the line is used as a system time constant in predicting the final temperature of the body. The time constant in conjunction with predetermined additional constants are used to compute the predicted temperature. Data quality in the time frame is monitored and if unacceptable, a different time frame of temperature signals is selected for use in prediction. The processor switches to a monitor mode if data quality over a limited number of time frames is unacceptable. Determining the start time on which the measurement time frame for prediction is based is performed by summing the second derivatives of temperature signals over time frames. When the sum of second derivatives in a particular time frame exceeds a threshold, the start time is established
