Terahertz (THz) electromagnetic (EM) wave emitters have been expected for applications because these waves are suitable for non-destructive inspection, telecommunication technologies, and other uses. Strong and coherent THz EM waves are known to radiate from large-sized intrinsic Josephson junction (IJJ) stacks in which the self-heating effect is considerably larger and the temperatures in the mesa are non-uniformly distributed. In this study, we numerically investigate and discuss the temperature and current distributions in large-sized IJJ stacks because these parameters are difficult to analyze through experimental investigation. The temperature and current distributions can be obtained by self-consistently solving the non-linear diffusion equation in an equivalent circuit of the mesa by considering the temperature dependence of several parameters. As shown in the numerical results, self-heating caused the local temperature of the center in the mesa to exceed the critical temperature. To improve the non-uniform temperature and current distributions, we propose an improvement in which an external heat generation system is placed on the edges of the mesa. By applying this measure, the temperature distribution is improved because the edges of the IJJ mesa are heated externally. Furthermore, the local temperatures throughout the mesa were held below voltage characteristics were improved using the proposed improvement.