High-precision laser radars and 3D vision systems with millimetre resolution require high-power picosecond optical pulses from laser diodes with direct current pumping in order to satisfy the requirements of low price, compactness and high reliability. A new laser diode capable of generating~50 W / 20 ps optical pulses for such applications has been proposed recently, but one very important technical limitation for many industrial applications lies in its repetition rate, which is at present limited to~50 kHz. This limitation originates from the heat dissipation in the Si-based, high-current nanosecond avalanche transistors used for laser pumping. It is shown in the paper, by using the 2D semiconductor device simulator, that the heat generation is powerfully localized in the avalanche transistor structure during the switching-on stage, but that in spite of this the associated thermal dynamics permits a higher maximum repetition rate than that observed experimentally. Moreover, smart designing of the semiconductor layers and construction of the heat sink should allow the limitation to exceed 1MHz. The lower limit observed so far in the experiments is caused by the stage of the voltage recovery across the transistor and may be softened by advanced circuit design.