Continous surging and stalling

Sounds like your coolant level might be low. At highway speed you probably have enough coolant and with the air passing thru the radiator keeps the temp down, but at idle not so much. Or depending whether you have a belt drive or electric fan. Belt driven, could need a new belt.

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

your car problem is overheating, some car model like yours is designed to shut-down engine when engine temp. rise so as to avoid frying the engine. your engine overheating problem is attributed by one of these factors:
1. check or refill radiator water if less
2.check radiator cooling fan operation-if damaged pls. change or check the electrical system.
3. damage/ worn water pump-if damage pls. change the water pump.
4. check for any coolant leak somewhere the coolant line-pls. rectify the leak.
5.worn coolant reservoir cap- change if damaged.
6. clogged radiator-if clogged pls. change it.
7. damaged thermostat valve.

Try and clean the throttle body. Carbon will gum up on the blade and the vaccume passages, which will cause a surge and stall.

Have your EGR valve checked. I just replaced one on a 95 towncar. It's my girl-friends car. It was $50.00 at Auto Zone. Local shops wanted $300. to replace it.

check the module and coil pack in the distributor

This is caused by a faulty temp sensor, look at the top of the engine coming out of the head right near the distributor there is a coolant housing with a coolant line which should have one maybe two sensors one will be black (square with 2 to 4 wires) the other one will be blue. If yours only has one connector then disconnect it, start engine...the engine may idle higher than normal drive it till it warms up or to the point where it would normally stall, if it doesn't stall then replace the sensor and problem solved.

If you have two sensors, black one and blue one, its been awhile for me but disconnect one or the other, one of them is your temp gauge sending unit can't remember if its the blk one or blue one. But try that.

Try The CTS sensor ( coolant temp sensor )

Here is the most common cause of surges and stalls, it is the idle speed control air-bypass valve and throttle valve, they get full of gunk over the miles and cause idle issues (stalls) like yours, Get a can of intake cleaner from any local parts store, not carb spray, intake cleaner, it is made by a company called CRC, remove the air intake hose to the engine, hold the idle high so the engine won't stall, then spray the can of cleaner into the intake while keeping the engine running, use at least 1/2 the can, shut down the engine and disconnect the battery for 5 minutes, then restart and complete a number of mixed driving cycles, town, freeway, stop and go etc., after a few days the problem will go away as the system will relearn to the clean intake.

Your ECT (Engine Coolant Temp) sensor is bad. What's happening is at cold start it richens up the fuel mixture and as it warms up the ECM thinks it's still cold and essentially the "choke" is still on. Also check your coolant level. If you don't have enough coolant in you engine/radiator, the ECT doesn't know what to do so it thinks it's cold.