Is the amount of rainfall in the Chihauhuan Desert dependent upon the average temperature or is the temperature dependent upon the amount of rainfall?

Answer 1

Temperature does affect rainfall in the Chihuahuan Desert. During the monsoon much of the rainfall comes from typical air mass thunderstorms. These storms form when there is high moisture content in the atmosphere and daytime heating causes convection that builds these storms. If the day happens to be cool, convection will be limited and these storms usually do not form.
High surface humidity will frequently lower the temperature as it takes more solar energy to heat moist air than dry air.
So the answer to your question is 'both.' Temperature can affect rainfall and rainfall can affect temperature.
It is not unusual to have heavy thunderstorms on one day and, even if the atmosphere is heavy with moisture, the following day there is little or no activity because the higher humidity is limiting convective activity.