Hello,
I just bought a 2011 XJL and I’m having some issues with the air conditioning. When I turn the car on with the AC on blast at Lowe’s warm moist air. After driving 5-10 mins it comes on. I’m thinking it could be the compressor. Thoughts? How could I test the compressor? And how much would the compressor take to replace?

 

Can you DIY any of this?
If not just take it to an AC shop.

Many,many threads on AC. Do some searches and see if they help?
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How's your battery health? Are your engine and chassis grounds clean?

 

Do a search on the DPS valve inside the compressor. I believe your symptoms are the classic ones for this valve having an issue. But from what I read, you might as well change the compressor instead of just replacing the valve. I don't know what the cost will be because I always do my own AC work to make sure it's done right, but shops do like to gouge customers on AC work.

 

Here is the TSB on the DPS issue

 

I also have 2011 XJL Supersport. My AC will only be mild cold for the first 10 minutes then get to the right temperature. What I also experience is the vent speed decreasing and increasing on its own while in auto. Is that normal?