The drill housing's temperature follows a lumped thermal-balance ODE: heat from drilling is removed by radiation (Stefan–Boltzmann) and, when the dome holds an atmosphere, by convection — convection scales with dome pressure, so venting the dome to vacuum removes your main coolant:
dT/dt = [ Q_drill − εσA(T⁴ − T_amb⁴) − h·(p/100)·A·(T − T_amb) ] / C
Sunlight reaching the solar panel follows the cosine law for a flat surface, so power collected scales with the sine of the sun's elevation above the horizon: P = P_max·sin(elevation).
Dust thrown by the drill bit is launched with a speed that grows with drill power, then decelerated by the asteroid's own gravity and — if the dome has any atmosphere — by drag. Whether a grain returns as usable regolith or is lost depends on how its speed compares to the local escape velocity, v_esc = √(2·g·R), for a fixed 500 m asteroid radius: low gravity (a few milli-g, typical of small asteroids) makes v_esc trivially small, so a energetic drill can throw material clean off the surface — a real constraint on real asteroid-mining designs.