Time the taking of your images so that the light levels from each source (artificial and natural) is the same, which will produce an evenly exposed shot. Take a spot meter reading from both the sky and an area of the shot that’s well artificially lit. When the sky is still slightly brighter, start shooting using the spot metered setting for the artificially lit part of the scene. Continue to take pictures using the exposures. You should have a few shots that are perfectly exposed during the ten minute window where the scene will be perfectly lit.