1998 Crown Victoria when you the hearter the engine surges the volt gauge goes up and down and the head get dim and the same time

this are is not a good location for a mechanical temp gauge
It is at the bottom of the coolant galley in the block and will be in the sediment that collects in a block
hot water rises and where you want it is where the water will be at the hottest ( bottom of the block is the coolest water) so select a point at the thermostat housing or a plug in the head that goes into the water jacket

Sounds like a regulator issue which is built into the alternator. New alternator.

It may be a bad battery, that is sinking power at some times and rejecting it at others. First check battery connections are firm tight and free from grease on the surfaces that join. If still a problem and battery is more than a year old, replace it with new.

on both sides of engine,on front and rear of cylinder heads and the dreaded on back of engine between motor and transmission

Sounds like the voltage regulator has failed.
Check voltage at the battery with the engine at idle and again with the engine at cruise speed. Voltage should be around 13 volts at idle and 14.5 volts at cruise speed.

bad iconic swich or bad coil

Notorious for intake leaks, the composite plastic intakes crack and leak coolant-as to the lack of power, you mght have overheated it and done some damage to the engine. There was a recall (information below) for the 4.6 for the intake-the overheating and lack of power means you should at least have compression checked and go from there-you may have bad head gaskets or worse. Do a compression test before you do anything else.

Ford Motor Company will extend the recall (01M02) on 4.6L V8 equipped vehicles with plastic intake manifolds. Some of the composite intake manifolds used on 4.6L SOHC engines may develop fatigue cracks at the coolant crossover duct. This condition could result in engine coolant leakage which, if not serviced, may cause engine overheating. Complete loss of coolant may result in engine damage or engine failure.
The updated recall now includes:
• Certain 1996 through 2001 Model Year Crown Victoria Police Interceptor
• Certain 1998 through 2001 Model Year Crown Victoria with Taxi
• Certain 1998 through 2001 Lincoln Town Car Limousine and Livery Prep Package
• Certain 1996-2001 Crown Victoria Taxis, Police cars and Lincoln Town Car Limousine and Livery cars.
• Certain 1996 through 1997 Crown Victoria Police Interceptor Vehicles with 4.6L SOHC engines built at the St. Thomas Assembly Plant from the beginning of production for the 1996 Model Year through January 28, 1997.
• Certain 1998 through 2001 Crown Victoria Police Interceptor Vehicles with 4.6L SOHC engines built at the St. Thomas Assembly Plant from November 22, 1997 through December 15, 2000.
• Certain 1998 through 2001 Crown Victoria Taxi Vehicles with 4.6L SOHC engines built at the St. Thomas Assembly Plant from November 22, 1997 through December 15, 2000.
• Certain 1998 through 2001 Lincoln Town Car Limousine Prep Package and Livery Vehicles with 4.6L SOHC engines built at the Wixom Assembly Plant from November 22, 1997 through December 15, 2000.

most likely not charging. Put a volt meter accross the batery when car is running. Should read at least 13.5 to 14.5 volts. If lower its not charging . Check for poor connection at battery connections .

ok, does the heater hoses that goes to the hearter core on your fire wall get hott, if so heater core is shot or one of the hoses r pluged or the heat selector by your fan or under dash is shot... an if your fan dont run kick it or its seezed, or a fuse.... sorry i dont no wat else to say..

pull the AC/Heater control head out and u will find a tiny peanut shaped bulb at the back of the dash display, replace it.