Peltier cells air conditioned system

In the hot 2018 summer I decided to build something to cool down my garage. I have no space for the external motor so I need to find a quick solution. The only thing I can do is to extract from the garage the air collected from a specific place.

Now i said ... why if I collect in that specific place all the hot air produced by a Peltier cell? or by a set of more Peltier cells?

I could cool down the hot part of the cell increasing the cold one on the other side.

For this reason I draw t