We had the same problem..Just turn off your water heater and after a few hours, The hot water side will be having luke warm or sometimes cold water which is comparatively much much better and bearable. So just turn off your water heaters and use the Hot side of the taps.
This is normal unfortunately. I use the hot water tap for warm water (water heater off during summer) and the cold water tap has steaming hot water. Nothing you can do about it unfortunately. You get used to it. Part of living in the desert.
The cold water comes from the storage tanks on the roof which get overheated in the summer. The hot water comes from a heater that is either visible in your bath or is hidden in the ceiling. Turn off the heater at the switch just outside your bathroom door. Use the hot water tap for cool water (the AC in your accomodation and the protection from the sun will allow the water to keep cool) and use the cold water tap as your hot during the summer.
OP, I know exactly what you mean, maybe you need to do one of these options:
a)Shower in the early hours of the morning, before the sun shows up, I know it's not that convenient but this is the only thing I could figure out ...Or;
b) turn the shower water for 50 min or one hour .... I know it's wasting water, but I did this before to shower the children....
c) just adjust the shower spraying very high, that water stream been interrupted with air, so it cools a bit, it was a bit effective if I was really need that shower, then I have a step stool I do sit down while showering....
HTH
Apparently it has something to do with the hot water pipes running next to the air conditioning, so even when you have the hot water switched off, the cold is still very hot, but if you turn the tap towards the "hot" side, then the water is coller (still not cold).
Turn off the hot water system in the house, then use the hot for cold and the cold for hot. We had to do this during the summer in our villa, couldnt figure it out but the water tanks heat up and the cold water runs hot hot hot.