You must live in an old building. My understanding is that you can't put the external unit on the facade. I live in a new building and we have floor cooling. I didn't expect it to be enough, but it's amazing.
Discussion
Floor cooling systems provide only a limited temperature range adjustment, typically a few degrees, compared to a standard wall-mounted air conditioner.
Vienna is an old city, with many buildings dating back centuries. However, this should not be used as an excuse. AC should come as standard like in the US.
