To increase the efficiency of laser oscillators by overcoming losses, the unsaturated gain must be increased. For this purpose, high-intensity pumping, typically higher than 100 kW/cm2, is effective. However, the temperature increase and strong thermo-optic effects of the gain medium have been pointed out as obstacles to high efficiency in solid-state lasers. Therefore, the effect of high pump intensity on the laser mode tunability required for high efficiency is investigated by studying the dependence of the laser threshold on the cavity length using a continuous-wave hemispherical short-cavity laser. The results show that the laser mode can be tuned with sufficient range and precision for high efficiency under various loss conditions regardless of the high pump intensity and are in qualitative agreement with a simple theory. Furthermore, according to the heat transport theory, microchip Yb:YAG, the gain medium of this study, does not have a high cooling efficiency, but the maximum temperature increase is estimated to be only about 12 K despite the high pump intensity of about 110 kW/cm2. This is because it is the pump power, not the pump intensity, that is proportional to the temperature increase, as the maximum pump power is only 900 mW. These results indicate that high-intensity pumping is a promising approach to achieve efficient lasing at low cost.