I was in Warsaw a month ago, staying at the Westin.
There is a Westin/Sheraton shared desk in the center of the airport arrivals hall to deal with transportation to the hotels. I inquired at the desk and was told the cost. I can't recall what it was, but it was significantly higher than a regular taxi, albeit in a much nicer car. The guy at the desk told me that taxis from the marked stand were perfectly safe and cheaper so I decided to go that route. I can't remember how much the taxi cost either, but it was quite reasonable. The ride took around half an hour in heavy traffic.