If your thermostat is working correctly removing it WILL NOT improve cooling and it could result in overcooling which will reduce your mileage slightly and cause increased engine wear.

If it is not working correctly spend the $5 or $10 for a new one.

By the way it sounds like your air conditioning needs to be recharged.

It's a mystery to me why some people think Goober down at the filling station knows better than the design staff in Stuttgart.