Car runnin hot immoblizes wont until cool offs

if no air in the system from internal heater or other places
new thermostat and radiator cap
good firm coolant hoses

old school air bleed
you fill coolant system with motor running
heater on in the car and thermostat open
burp the hoses until bubbles are no more

if still no better
what about these possibles
faulty coolant temp sender
head gasket failed
clogged radiator
cooling fans not spinning fast enough
or not coming on soon enough

disconnect the heat hoses going into fire wall , put hose into one with pressure and flush as it sounds like it could be bloked in the heater core,the other thing that could be the problem be the hot ,cold switch as it restricts the flow to makes the heater hoter or colder , it might need tlc or replacing as it is manaul not elec

FAULTY COOLANT TEMPERATURE SENSOR OR IDLE AIR CONTROL VALVE MALFUNCTION.BEST TO GET CAR CODE SCAN THAT WILL SAVE TIME MONEY AND GUESSING.

I would check to make sure the radiator is full and the overflow tank is filled to the proper level. It doesn't have to be very low for these cars to stop blowing heat.

You'll only see good circulation when it's at operating temperature & hot enough for thermostat to open, allowing coolant to flow through the system. Hope you had heater on (not defrost) while you were letting it run/circulate. I usually wait for rad fan to come on 2 or 3 times, before I put cap back on. Rad fan comes on to cool what just came out of engine when thermostat opened, so when you see good flow, you'll probably see fan come on shortly after.

You may have an air pocket in your system which some times happens.  One way to get rid of it is to take the upper hose off on the engine side,  fill your system with water until it runs out from your engine block, replace the hose, start your car turn you heater on and set to hi keep the radiator cap loose until the temp start to rise then close tight.  Once the air pocket had been remover you can drain some of the water from the radiator using the lower drain plug and add antifreeze.   

ya the fuel pump wont pump with the lines off but the pump is going bad they will work and wont work

You have a bubble in the cooling system that is blocking the thermostat from opening. Alleviating it is simple. Now that you've changed everything, just jack the car up so that the thermostat's opening is facing slightly upward. Start the vehicle and let it idle until it's about 3/4 of the way to hot. This is how you'll know the bubbles are trapped behind the thermostat and keeping it from opening (you want it facing upward so that the bubbles will stay behind the thermostat and not move off away from it). Once you reach 3/4 hot, shut off the car and go have a beer while it cools off. Once it cools enough to safely open the radiator cap, open it up and the release of pressure will allow the thermostat to open. The bubbles will come through the thermostat and "burp" out of the radiator (which you may or may not see, but it will happen). You may see the level of coolant drop somewhat, since the air bubbles were taking up space in the cooling system. Top off your coolant both in the radiator and the overflow reservoir if yours has a fill cap, put the cap back on the radiator, and you are good to go. With the bubbles burped out, your thermostat will be able to open and close as needed and the cooling system will operate as it should.

Check for a vaccum leak at the intake. Frankster016

Not sure if there are two thermostats, I know of one that I changed, it sits right above the starter and right below your air box. I had the problem my guage was reading hot on a cool night so I went and popped the hood and (after cooled) opened the radiator resivoir and the results were dry as a bone. I had steam coming from the cap. if you so this be sure to slowly release the pressure from the red cap that reads HOT WARNING DO NOT REMOVE. that is where you pour the coolant/water mix.

After I did that I took it to a shop and had it flushed, cleansed and refilled.....then I was runnin a beutiful bright green. Cost about 69.99 for flush then I found out my water pump pully was locked up and not rotating (not pumping coolant). So I fixed that last night and she's runnin pretty good after 190,000 miles.

Good Luck Mazda's