RENAULT ESPACE LL 1994 Air conditioning

Although it's quite old, I rebuilt the engine 7 years ago and it's been regularly serviced.
The only problem I have is with the air conditioning. It cools well until the engine reaches operating temperature, then it starts blowing hot air.
If I turn off the AC but leave both cooling systems running (I have a separate control) and lower the coolant temperature, then turn the AC back on, it cools normally until the coolant heats up again. I know they're two separate circuits, but I don't understand why.
Any suggestions?
Thanks.

I'm asking
when the AC is on, do the fans turn on automatically?
Or do you activate them yourself?

Thanks, Antonio.
I've discovered that the problem is with the second speed on one of the fans.
I've swapped the two relays it has, and they seem to be fine. I need to find two more, as I think one is faulty.

Okay, fixed.
Of the several relays it has, I swapped a couple this morning and found one that wasn't working.
€4 and it's fixed
. The problem was that when only one fan was running, the temperature rose
excessively and the AC cut out.
Thanks anyway for your interest.
Regards