Thanks for the responses.
My prob is, that room temp is between 80 and 88 F depending on the season and day time.
I understand that if I want the starter not too become overly acidic i need to cool
- aircon 24 hours is not the right way (too inefficient and a waste of ressources and money)
- cooler box with ice. i tried it and will come down to 73F. => is this too high for the yeast to develop ?
- for storage i can use a fridge, but of course consider warm up and proofing
- other technical solutions: at the moment i do not know where to get all the sensors and stuff to build it. where i live atthe moment there is e.g. No DIY store and noone cold tell me where is the little special shop, that sells items like temp sensors etc.
- wine cooler: well, i do drink wine here and then and enjoy, but to acquire a separate wine cooler and then store my dough and starters in it...mmmmhhh here i have consensus issues

So i think i will try to go for the fridge and cooler box solution and try figuring it out, how much time i need to proof. Hope when i am ready to bake pizza from the Ischia starter it won't be too acidic.
But i will see and learn and it will be alrite. Thanks