Cooling a vehicle in the AZ summers can be a challenge.......I moved out here 30 years ago and it's been a learning curve ever since.

As far as a secondary radiator......I did that once (52 Ford F6....big truck with a lot of under under hood room)I installed a complete small radiator with it's own cooling fan. It was a colossal waste of time! the only thing the second radiator did was cause it to take a little longer to get to the same temperature it got to before.

It's really kind of hard to make any suggestions without knowing what you're currently working with. What temperature does it run at in the summer. When does the heating occur; in town or going down the highway. Have you verified that the temperature the gauge is showing is accurate (I've had gauges read as much as 30 degrees off).

It would also help to know what type of radiator, number of tubes and with width of them. What kind of fan and do you have a shroud. What is the temperature range of the thermostat.

Pictures would help too.