Engine Overheating while I drive?

Every thing is linked through the alalrm system. It may require a reset by the dealer.

It's true that the heater core is behind the dash, but $600 sounds ridiculous to put in a heater core. The core itself only costs about $30 retail, which means he probably gets it for half that which means he's charging you basically $600 in labor. In my opinion, a heater core replacement on a scale of 1-10 is about a 6. I'd get an estimate somewhere else, or even try to do it yourself. The hardest part is getting to it. After that, it's simple.

Would you explain "overheating" what happens?

New headlights bulbs in a effort to have brighter headlights actually run hotter.

As with anything that generates heat, it is not only the heat generation that could cause a problem, but the lack of heat dissipation. Take for example a computer power supply, we know it generates heat, that is expected, it becomes a problem when the fan stops and the heat increases.
So, if you did not change the bulbs, what changed the staus quo of heat exchange.
Most headlamps assemblies on the taurus are plastic, even the lens.
If both high and low bems are on simultaneously that might do it.

So take a look again please.

Could be air in the system, clogged radiator and water pump if all okay get it block and pressure tested.

Have you changed the thermostat?

Make sure the level is full and the radiator fans are turning on.

Defective water, clogged-up radiator if both okay get it block and pressure tested

If you have never changed the coolant it ois probably a clogged radiator. Old Ford coolant is bad about that. The rad can't be cleaned so it will probably need replacing as well as the thermostat. Use the same T-stat temperature.

The battery light sounds like a bad alternator

Overheating no heat is an indication of low coolant check coolant
and check for leak

Does it get hot at all speeds or just in traffic? Also, have you tried flushing the cooling system? Are the cooling fans coming on?

Let me know.

Joe

Is this a 1997 Ford Taurus V6-183 3.0L DOHC VIN S MFI?