Has stalled while driving to work won't start untill it cools down for 2hrs. or so. temp. reading is just alittle over half way mark when shut down occurs don't hear fuel pump when it's in stall mode.

Radiator cooling fans not working? The ECM is protecting the engine by shutting it down.

first look to see if the cooling fan(s) come on when the temp gauge reads hot or above half way mark. I suspect the coolant temp sensor is faulty and not sending correct temp reading to pcm and is not turning on the cooling fans.. other possibility is the cooling fans are burnt or relay to fans also ..I would check fans first then relay info back here for more advise.

98 and 99 intrepid was manufactured with weak fuel pumps causing them to vapor lock try pouring cool water on the fuel rails on the intake to calm vapored gas then try to start it. Even the temp gauge at half way mark is probably still low on coolant causing engine to be warmer than normal causing the vapor lock to fix this problem replace the fuel pump with a 2000 or newer intrepid fuel pump that carries a little higher psi to prevent vapor lock from reoccurring this pump is compatible with your 98 it will plug right in

You'll have to figure out if it is a fuel or ignition problem.
Is the check engine light on ?

I am thinking that perhaps the temperature sensor is reading wrong and therefore sending a message to the computer that the car is running too hot. This can happen, my VW presently reads 20 hotter on the guage than a heat gun records at the temp sensor location on the head. If you have access to a heat gun it might be a good idea to check out the actual temperature, but it probably won't hurt to change the sensor.

The other problem that occurs to me is the oil sending sensor. While a temperature sensor won't shut an engine down, the oil sender can. If it is reading a large drop in oil pressure it will shut the engine off. Since oil gets thinner as it gets hot, perhaps a defective sending unit is reading it as too low. Once the oil cools off, it would restart until the temperature gets too high again. I would think that upgrading to a heavier oil might cure the problem. I don't know what you are currently usung but certainly you could go to 10W30 or 10W40 without too much trouble, at least for a test. Hope this helps.

It may be running because the engine hasn't cooled down. These fans will run until the engine reaches a specific cool temp. But if it's not running hotter than normal temp, it's within the temp switch, which reads the temp of the engine, or the relay could be bad and not know when to shut down. While you're driving look to see what the temp gauge is reading. This will lead you in different direction for the temp. switch.

i wonder if possibly a defective thermostat, that it is sticking open.
to bench test thermostat place in a pot,if you have a candy thermometer all the better ,place in cool water and bring to boil checking temp.it should open alittle at a time until being fully open at what ever temp it is rated at
then slowly add cold water and it should close in a similar fashion

My 2003 nissan sentra would get hot and stall out even in middle of highway doing 70 mph. The guages would go up and down. Would not start up all the time after stalling. had to cool down first. Nissan said it was head gasket, and wanted to charge 1000.00 for the job. I took to local dealer who charged me 550.00. Works fine ever since. Nissan dealer said they do like 3 head gaskets a week on the sentras. They have crappy ones in original parts. They have not recalled though.

Is the temp guage reading high or are you just suspecting it needs to cool down? Could be thermastat bad or possible water temp sensor bad. Maybe water pump. After next time you run the car for awhile carefully touch the radiator cap and should be hot, if not then coolant is not circulating.

replace the fuel filter