perhaps we have a scientist who posts here and can explain how many degrees difference pulling the blinds down will actually make
It is not just a matter of temperature difference. The important issue is thermal energy entering the cabin.
Cabins are designed to minimise conduction - they have to cope with greater than 80K temperature differential. Windows allow thermal radiation.
Insolation is typically in excess of 1000w/mē on the earth's surface (assuming 30° sun elevation) - up to double that on a sloping aircraft window. With an area of 0.1mē per window that can be over 10kw for 50 windows.
10kw is not an insubstantial amount of
extra energy to remove (cool).
Closing the blinds will not reflect all the heat but a high proportion.