I have EXACTLY the same problem! I have not looked into it, but now that it is getting warm out, it is time. I suspect that it is vacuum controller behind the glove box.
Could someone here confirm this as a good starting point. How can this be tested before buying a replacement?
'05 E320 CDI - 86,000 miles
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'85 300SD - 317,000 miles (sold)
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2005 Tzitzu (Griffon)
2009 Welsh Corgi (Buba)