Hi to all
I have been the same problem, compressor work good under 38 º C, and when the Temp is higher and drive on the city (slowly), shut down. I need to switch off the AC swith for 10/15 minutes and cold air again for other 5/10 minutes.

I reed many post about this matter and yesterday I did some test in my car (190.000 km).
I bypass the overtemp compressor swith, no result beacouse today in not very hot in Madrid (Spain).

One think that is not claer to me is the nature off the black block, side by side with the compressor and in serie with the clouth. Many people said that is a diode to cut overvoltage to the A/C relay.

With a ohmeter I test this diode, and two posibilitis, my diode is wrong, or the black box is not a diode.

The resistance mesured from the input of the black/box to Batery (-) is 3.6 ohms, that is the serie circuit off black/boss plus coils/clouth.

Really to put a diode in serie with a coil is not a good idea to avoid interference from the coil to the AC relay at the time of swith off and do not avoid the electric arc at the relay contact, better idea is in antiparalell configuration.

My theory.

The clouth is operated trouhg a DC coil. In order to not oversize this coil is necesary to reduce the higth initial current (4Amp. more or less) trough the coil to engage the clouth, to a mantenence current enought to keep it engaged. That task is do it by the Black/box.

From my point of view the Black/Box is a PTC resistor (PTC= positive temp coeficient). Initialy has a low resistance and the current is high, and by the effect off this current (desired effect) and ambient temp (not desired effect) the black/box increase it temp and it resistence and decrease the currents trough it and trough the clouth coil.

With a amb. temp very higth and some time passing current, the PTC resistor as a ohm resistance very higth and the current becomes below the mantenence current, so the clouth is mecanichaly removed, but electricaly engaged. that is way we need to removed de AC swith to cut the current to cold the PTC.

With the time probably this PTC change slowly its performance and become the origin of the problems.

Be carefully to short circuits this black/box, that could damage the clouth coils, not immediatilly but in no many time.

That is my theory, probably wrong. I will try to test it in the next days.
Comments will be very apreciated.
One more think, I apoligize you for my terrible English gramatic
Regards

One more consideration, the solution point to a resistor in paralell with the PTC ( Black-box), I need to do some test to define its performance.