Engine heating up after turning off

AS FAR AS THE OVERHEAT ISSUE BLEED THE AIR OUT OF THE COOLING SYSTEM. FOR THE NO HEAT CHECK OPERATION OF TEMP BLEND DOOR AND FOR CLOGGED HEATER CORE

The thermostat is a critical part of your coolant system, the system that circulates water and antifreeze (coolant) through the engine to keep it from over-heating. It is called a valve because it can open and close, depending on how hot the coolant is acting upon it.
The reason to put a thermostat in the coolant system is to allow the engine to reach normal operating temperature quicker (and therefore operate at peak efficiency) than without a thermostat.
When the engine is cold, the coolant is at normal outside temperature, so the thermostat is closed. This means when you start the car, the coolant starts circulating through the engine, but can't flow into the radiator. With a closed thermostat, the coolant just keeps circulating around in the engine until the car warms up, the coolant gets hot, and the heat acts upon the thermostat, causing it to open at a certain temperature (about 185-195 degrees F.), With the thermostat now open, the coolant can now enter the upper radiatior hose and flow down the radiator to cool itself down, before going back into the engine through the lower radiator hose.
So the thermostat is always found on a car in the area where the upper radiator hose connects to the engine. Thermostat closed-water can't circulate through the radiator. Thermostat open- coolant is forced through the hose into the radiator.
I hope this helps you understand the thermostat valve and why all manufacturers include them.

http://www.freeengineinfo.com/s-10-thermostat-replacement.htm

Please see link above.

1. Make sure the engine is cool.
2. Using a clean bucket disconnect the lower radiator hose and carefully drain around 1 gallon off coolant then reconnect hose.
3. Follow the upper radiator hose to the engine where it's connected to the gooseneck on the engine.
4. remove the 2 bolts holding the gooseneck and lift it up to remove the thermostat making a mental note on how it was installed.
5. Clean both sides of the gasket surfaces, install new thermostat in the same position it was removed and replace O ring(only use a Motorcraft replacement to avoid having fit issues) alternate tightening bolts until tight.
6. Refill radiatior to proper level.
7 Leaving the raditor cap off, start the car turn on the heater and let it warm up keeping an eye on the coolant level, it will go down once the air works it's way out of the cooling system.
8. Top off the system and tighten radiator cap. Check the coolant level several times during the week, there may still be some air left in the system.

CHECK COOLANT LEVEL STILL LOW.ADD MORE COOLANT.UNTIL RADIATOR OVERFLOW FULL AT COLD MARK.THEN CRANK ENGINE UP LET IDLE FEW MINUTES LOOK DOWN COOLANT OVER FLOW JUG ADD MORE COOLANT IF LEVEL DROPPED.WHILE ENGINE RUNNING KEEP EYE ON TEMPERATURE GAUGE.WHEN THERMOSTAT HOSE GET HOT.TURN OFF ENGINE WAIT A LITTLE WHILE TO KEEP FROM GETTING SCALD TAKE LARGE RAG PLACE OVER OVERFLOW JUG RADIATOR CAP.OPEN CAP A LITTLE A TIME.IF COOLANT TRIES BOIL OUT.LET VECHICLE SET A WHILE LONGER.ADD MORE COOLANT.WHEN COOLANT LEVEL CORRECT AND ALL AIR OUT THE COOLANT SYSTEM.IT WILL STOP OVERHEATING.LONG AS ENGINE RUNNING HOT TURN OFF THE ENGINE POUR IN MORE COOLANT UNTIL COOLANT LEVEL STOP DROPPING IN RADIATOR.KEEP COOLANT LEVEL IN OVERFLOW AT COLD MARK.DONT OVER FILL OVERFLOW JUG.

You will need a couple of tools, and they are ratchet, and extension, and some metric sockets, a scraper, and a flat tip screw driver. I do have a question, before going to the auto parts store, are you hoses 3 years or older? If so, change them now also. Now lets get a new thermostat, gasket, and gasket sealant. If changing hoses, 2 hoses, 4 hose clamps,and coolant. Now, remove the upper radiator hose at the engine( this is the thermostat housing cover). now, remove the 2 bolts securing the cap to the engine block. now, gently pry up the housing and stop. turn the cap over and scrape it clean, to shiny metal. now do that at the engine block. Clean, great(you don't want any way for the cap to leak), now trade out the thermostats(I had you leave the old one in for cleaning, to keep anything out of the engine), now take some gasket sealant and put a thin coat around the engine block where the gasket goes. take the cap and do the same. place the gasket on the engine block, and carefully set the cap back on. put the bolts back in and connect the hose. and you are done. about 30 minutes for a beginner. another 20 to change the hoses and and fill with coolant and water. start the car, and let it warm up, wait for the thermostat to open. (you can buy a new one, that is broken. it happens) check for leaks. No leaks, great job

How is the interior heat? Is it normal or are you only getting about 1/4 of what it used to be like when it was newer? Are you running a summer thermostat or a winter thermostate? The thermostat may be defective and not closing all the way and needs to be replaced or the Coolant Temperature Sensor may be Defective and needs to be replaced. I love these cars. Good Luck and have a good XMASS.

if you find top hose follow it to engine -thermostat housing have to bolts most times /1)drain coolant 2)take about bolts pull up housing take out thermostat 3)put thermostat in (note;how thermostat is turned put new one same way) clean housing good 4)put gasket on with little bit of sealant tigthen bolts 5)put hose back on 6)fill up radiator with coolant &let run till warm up [check for leaks while warming up }top radiator off ;;;;;done

Check coolant levels in the radiator and the overflow resevoir. You may have blockage in the radiatior and you could have a sticking thermostat.