In my own experience, you can do some amount of heat management with those shutters and the window by chosing when you have them open and when you have them closed - whilst without aircon the appartment tends towards the average temperature of the whole day, you can push it a bit more one way or the other by managing sun exposure and air circulation in favor of the hours when the temperature is more towards the end you want.

What I did were I live during the last heat wave (which around here had max temps above 40C) was to during most of the day keep the shutters down and the windows closed, and then during the night and in the early morning having the window open and just the holes of the shutters open (the shutters are made of strips and the are some holes between them, so when you pull them up they first just open the holes and only after all the holes parts of the strips are exposed if you keep pulling them up wil the shutters lift up - example)

In simple terms, during the hours when the sunlight would hit my windows it was hitting the shutters instead and either being reflected or converted to heat outside rather than inside (as those shutters are installed outside), and air was allowed to circulate between the outside and inside only when it was colder outside.

That said, for a couple of days I had to help the air circulation during the colder hours a bit with a fan, since just passive circulation through the half-open shutters wasn’t enough.

This way I managed to keep the inside temperature mostly below 30C, with no aircon.