OK, more details.
If you look closer on the EDP, you see 3 hydraulic lines connected to the pump.
The supply line from the reservoir, the pressure line to the system and ... the case drain.
There is a small flow through the pump housing for lubrication and cooling purpose.
These case drain flows even when there is no system demand/flow.
But the case drain goes not go back directly to the tank. It is routed via 2 heat exchanger (case drain to fuel) in the wing tanks.
Without fuel in the tanks the complete system is getting to hot.