Off, with a cold engine.
Turn it off. Let it cool off and then see if it has a coolant leak or radiator leak. Don't open the radiator when hot because the hot water will spray out.
You can turn on the heater as that will cool the coolant more. If the car is sitting still and off, opening the hood will help. If you have a hose available..spraying the radiator with help drop the coolant temperature by increasing the radiator's efficiency.
Take the cap off the radiator and open the petcock on the bottom of the radiator.
Do it when the car is cold if the radiator is hot fluid may be forced out when you take off the cap.
There is a petcock on the bottom corner of the passenger side on the radiator. If you turn the petcock and open the valve the coolant will drain out of the drain hole on the bottom passenger side of the radiator. Make sure you have a big bucket to catch the coolant in or you will be making a huge mess. The proper way to fill the radiator is to take the upper radiator hose off and pour the coolant in until the radiator is full. Then replace the radiator hose and fill the overflow to the correct level. Start the car and let it run till it is hot and the fans kick on (should be about 220F ~ 230F). Turn the car off and let it cool, then top off the overflow bottle. You should be fine to drive the car at this point, but after heating up the car again you may need to top it off again so keep some coolant handy. The cobalt uses dexcool.
open the plug (screw) at the bottom of the radiator, open the radiator cap and let the system slowly gravity bleed while pouring more fluid into the radiator. do this with vehicle off.
Deep down right side near radiator hose yellow color you be better off reach it when you lifting the car for oil change
Sounds like you have radiator trouble. Have you checked the fluid level in the radiator?
Almost all Mazda's have a drain plug in the bottom of the radiator. Easy to see if you just look under the car. You do not even need a wrench. It is a low spot and almost all the fluid will drain if you just open the radiator cap. Almost all moder car will need to be "toped off" a couple of times when you refill the radiator.
open your hood. take off your right side headlight bezel. remove headlight and park/turn signal light. your radiator pepcock will be in plain sight. remove your radiator cap and open your radiator pepcock to drain.
you need to get the engine checked
yes, anytime you have to take a radiator out of an automatic car the tranny lines have to come off the radiator.