Engine overheated when air conditioning is switched on

Hello everybody, my 95er 9000 comes with a high outside temperature plus traffic jam plus the air conditioning that it steams out of the engine compartment. It can’t be the cooling system, because the temperature indicator doesn’t rise and the cooler system has also been checked and rated for functioning – so nothing striking. If you turn off the air conditioning system, you can simply continue driving. Does anyone of you also know this phenomenon or the cause?