Lack of Freon sounds very far fetched to me. But there should be an easy test to rule this out.
Turn off your A/C. If you set the climate control to Automatic, the Boxster will run the A/C 100% of the time when the temperature is above freezing. So you'll need to manually turn it off (press the snowflake button on the climate control). With the A/C off, it shouldn't make any difference if the system has Freon or not. Yes, the serpentine belt will still turn the A/C compressor pulley, but I believe there is a clutch mechanism that disengages the pulley from the compressor, so it will just be freewheeling the pulley. If the Freon is really the problem, then it should go away without the A/C on.
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Demick
'04 Boxster S
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