An analytical study of random temperature of lumped system by FPK method, under the boundary condition of heat convection and radiation is carried out in the paper. The random temperature excitation is assumed to be white noise with zero-mean value and the system time constant is supposed to be a constant. Under the boundary condition of heat convection, the random temperature of system obeys normal distribution. The mean of random temperature of system is zero, and the variance is inversely proportional to square root of timeconstant. Under the boundary condition of radiation, the random temperature of system does not obey normal distribution. When applying the above theory to temperature measurement by thermocouple, the random variation of thermocouple temperature relates to the time constant. The precise measurement of dynamic temperature is impossible when there is random excitations.