If you want to keep it cool inside, you have to somehow insulate the interior spaces against heat influx. Insulation is created (among other things) by stationary layers of air. It is better to regulate such a stationary air layer outside, in front of the window. In this case, with the help of the roller shutters. Unfortunately, the material of today's roller shutters is no longer as insulating as wood used to be. Wood already contains stationary air layers within its structure due to the capillary structure in the wood.
If it is not or only limitedly possible to create a stationary air layer outside, then you can do it inside. A cloth casts a shadow. Linen or other rather semi-transparent fabrics do that as well. Then a quasi-stationary air layer builds up between the window and the cloth inside. It can get quite warm there and the heat is only slowly released to the interior. Theoretically, it would be even better to hang two layers of cloth with some distance in between.
I simply took cotton fabric from Ikea for 4 euros/meter. I hang it double (because of the air layers in between :D) and it creates "filtered" warm white to yellowish light in the room. At 30° or more, it's worth it for me to sit behind curtains.
At night, you can then, preferably with cross-ventilation and the ventilation system turned on again, air out the warm layers of air. And then the next warm day can come.