We measured electrical shot noise in a metal-insulator-metal tunnel junction, which was made by using electron-beam lithography and double-angle evaporation technique. Since the dependence of the shot noise on bias voltage and temperature is theoretically well known, we can determine the temperature of the junction by measuring the noise as the voltage across the junction is changed. A cryogenic low noise amplifier was used to amplify the noise signal in the frequency range of 600-800 MHz, which enabled fast measurement of noise signal and thus temperature. With further study, this method could be useful for primary thermometry in cryogenic temperatures.