How do you calculate the thermal rating of a worm gear drive?

Worm drives have low efficiency (40-90%), generating significant heat. Thermal power rating Pt = K.A.(t_s - t_a), where K is heat transfer coefficient (13-18 W/m2K natural convection, higher with fan), A is housing surface area, t_s is allowable sump temperature (80-90C), t_a is ambient. Mechanical power rating Pm = Pi x eta where eta = tan(lambda)/(tan(lambda + phi)), lambda is lead angle, phi is friction angle. Actual rating is minimum of mechanical and thermal ratings. Cooling fins, forced convection, or oil coolers increase thermal capacity.