2000 Chrysler LHS - Is it overheating?

I have a 2000 LHS with 137,000 miles on it. I
acquired the car when the previous owner
had given up trying to fix what seemed to be
an overheating problem. The car has been
impeccably well maintained and for the last
6 years it was only driven during snowbird
season (about 4 months out of the year). It
is a gorgeous car and I was willing to pay to
have it fixed. The previous owner had
replaced the water pump, timing belt and
thermostat. Whenever the temp gaug3
started to rise, he pulled over and to his
account, the car had never actually
overheated.
Like I read in another question on this site,
my car will run at normal temperature for 5-
10 miles and the temp gauge will start
rising. It never loses power even when the
gauge says the engine is too hot. And the
temperature will go back to normal quickly
when any one of several different things are
done. Turning the heater on, obviously.
Punching the gas pedal and keeping the
RPMs high for a few seconds. Putting the
vehicle in park and letting it idle. Putting it in
neutral and revving the engine to about 3500
RPMs for a few seconds. All of these things
will drop the gauge to nearly normal
operating temperature. It never loses power.
It has also never had a heating event that
caused coolant to steam from the heat of
the engine. We've not noticed any coolant
loss or seen evidence of engine oil in the
coolant or vice versa. All fluids are full and
clean. No problem with the AC or heater. No
squealing of any belts.
I took it to the dealership because I figured if
anyone could diagnose the problem, they
could. They did their usual preliminary
diagnostic tests and the related sensors
were sending the proper signals to the PCM
and the cooling fans were functioning
properly. They tested the cap on the coolant
reservoir tank, etc. They said there may be
an issue with the coolant flow and wanted to
replace the thermostat. And if that didn't
work, they wanted to replace the water
pump. Both repairs had been done
previously but they would not do further
diagnostics until they replaced the
thermostat. So I authorized the repair. And it
still had the overheating problem. They did
some sort of pressure test that measured
the gases in the engine (?) Or was supposed
to indicate a cracked block or something to
that effect, but the test results were normal.
Honestly, I tuned out after they said
replacing the thermostat hadn't worked. The
next steps would be to replace the water
pump again. And if that didn't fix it, taking
the motor apart and sending the cylinders to
a machine shop to have them measured to
see if they were warped. Whatever. I had
them return the car to me.
It runs the same as it ever did. Strong even
when the gauge pegs up. No loss of power.
All systems operational.
I am at a loss. My husband keeps telling me
"The car is not overheating. It's the gauge".
But then why would doing any of the things I
mentioned earlier cause the gauge to drop, if
the gauge wasn't working to begin with? And
how do I know if it IS overheating if the
coolant doesn't boil up and out of the
engine? Are there any electrical type
components that should be replaced
alongside replacing the gauge?
Sorry for the long post. I'm truly at a loss and
I really hope someone has an answer. Any
answer. Thank you.