Yes, that depression is where the oil cooler (the round central element that's most visible in photos) will sit. The cooler sits forward of the radiator face by approximately six or eight inches. Here are two of the photos that will hopefully add to my explanation.
In the first picture you can see the round fairing that ducts air into the oil cooler with an angled piece above it that leads upwards and forward. This is a return line that leads from the front of the engine to the radiator front face, terminating just above the oil cooler.
Hawker Tempest Eduard 1/48
In this uncowled photo the oil cooler is not installed, exactly as in the picture you posted of the Hendon airplane. The return line is visible in this picture, leading to its location above the missing cooler and its fairing.
Hawker Tempest Eduard 1/48
Clostermann's airplane was a Tempest V, so it will have this exact system on it. The VI moved the oil cooler from the radiator "beard" opening to the wing roots.
Sorry if I'm making it more confusing. Perhaps take a few photos of the kit parts and we can talk about what you have to work with.