As is well known, base region is the design focus of bipolar junction transistor (BJT). Generally, the doping distribution in base is non-uniform. In this paper, the effects of different Gaussian dopings in the base on bulk temperature distribution, temperature dependences of current gain and cut-off frequency are first studied. It is found that current gain and cut-off frequency of BJT have positive temperature coefficients, and the temperature in bulk is high. Then, the effect of Ge composition distribution on these device parameters is investigated. It is found that the SiGe heterojunction bipolar transistors (HBTs) with box Ge composition distribution and trapezoidal Ge composition distribution have negative temperature coefficients of current gain and cut-off frequency, and have good bulk temperature distributions. Furthermore, the SiGe HBT with trapezoidal Ge profile has higher current gain and cut-off frequency, and its temperature insensitivity is kept. The good trade-off is made among the magnitudes of current gain and cut-off frequency, temperature sensitivity and bulk temperature distribution.