I drive my junk here in AZ when ambient temps are 100-112 and don't have any rising coolant temp problems. This was with 4 row copper brass radiator, Hayden heavy duty fan clutch, 7 blade fan, 4 1/2" water pump pulley.
Here,s the check list...
1. water pump divider plate clearance. You want the impeller as close to the divider plate as possible. Use hammer and hammer the plate all around the part that sits over the impellers and account for thickness of gasket. Also make sure you have the tubes that fit inside the timing cover and good rubber seals to seal the divider plate.
2. Check the radiator is not plugged with corrosion. Radiators do not last forever.
3. fan shroud is a must as is a thermostat.
The big factory water pump pulley doesn't spin the water pump fast enough for idling around traffic. Never use tap water it has to many minerals. If you use distilled water without any commercial anti-freeze/ coolant you must use an anti corrosion additive.