For those who can be interested buy this problem, here is the end !
My local MB dealer finaly fixed the A/C. He confirmed that THERE IS a relation between the external temp and the temp of the air send by the A/C. The hotter is the outside air, the colder is the air send by the A/C, to improve its action inside the car.
So, the failure came from a bad connection behind the instrument panel, that appeared only when the back of the instrument panel was very hot. MB changed the entire instrument panel (at no cost for me, great !), and now everything's all right.
Long life to MB !