Lately, when I start the car in the morning or after a long parking, I hear a rattling sound roughly from the radiator area. It happens only when the climate control unit is on. The sound appears in about 20 seconds after the start, and subsides in about 90 seconds. If I switch off the CCU, the sound doesn't stop immediately, but rather subsides in waves, as if something is winding down.

So, obviously it has something to do with the CCU, but what can it be exactly?

I'd be looking at either the condenser, or the compressor.