therrmostat
 

is it ok to run my car with out a thermostat here in AZ

No.

If you are planning to run without one, you need a restrictor plate at the very least, or your engine will have hot spots and improper cooling.

restrictor plate? sorry im a newbie

Just leave the thermostat in, or if you have to get a new one get it from Mazda only. There's no good reason to leave it out, only potential problems.

Basically, if your car is running so hot you think you need to pull the thermostat, there are bigger cooling issues to be solved. Considering the age of the car, you probably need a new radiator.

One thing to add, if you elect to remove your thermostat you must also make some other modifications to the car to reduce the chance of screwing up the engine. You should also remove either the fuel pump or all 4 spark plugs. This is critical so that you won't damage your engine. The working principle here is that removing the thermostat makes as much sense as trying to run your car without a fuel pump or spark plugs!