In my experience, about the best you can hope for in an aircraft hangar is something the USAF defines as a "Controlled Area", or a "Class 300,000 Clean Room". Those standards include the following:
* 300,000 0.5 Micron particle count,
* 80 deg. F., 50% RH max,
* 2-stage filtration: 50-60% rough filter followed by 80-85% final filter, and
* minimum 10 air changes per hour.
They also include positive pressure in that list, but as noted, that should be an exception. This comes from USAF "T.O. 00-25-203, Contamination Control of Aerospace Facilities, U.S. Air Force", which was revised 3/85. My copy is most certainly out of date, but I doubt that the particular items we're discussing have changed that much.
Obviously, "Clean Room" as we normally think of it (such as in laboratories and semi-conductor production) involves drastically more complicated measures.