Just a thought but does your car have "cabin filters"? I know if the filters are dirty they can cause the system to ice up. This may be the case since you are getting ice cold air to start with.

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Dennis
2006 E320 CDI Black/Black Leather. Nav, HTD Seats HK stereo 32000 miles.
2000 VW Passat 1.8t 300,000 miles as of Dec 09, 2009 original owner
1997 E300d Silver 300,000 miles As of Jan 05, 2010
3rd owner SOLD