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My AC just works fine while driving > 20MPH. However, when I stop at traffic signal , its starts blowing hot air. I checked the fan and it works, I think there is only one cooling fan for both condenser & radiator in XJ , I am not sure. AC refrigerant pressure tested and there is no leak .
Possibility could be A/C Compressor, sounds like its weak. Did you have the operating pressures checked while running? Should be around 150-200 psi on high side, and around 20 -25 on low side at idle, when compressor is cycling.
20-25 PSI on the low side seems somewhat low. I recharged the AC system on my 2005 Jaguar XJ8L last week with a resulting 38 PSI on the low side, and the air conditioning still worked great.
The low side pressure will vary with heat load and ambient temperature. Generally it needs to stay above 23-25 PSI to avoid evaporator icing. The thermal expansion valve will do this. The compressor on these cars does not cycle like a CCOT system.