Hey, Mike:

It's not always the operation of the guage, but the efficincy of the
cooling system and the heating system as well.

Ever live in a house with small pipes? You're taking a shower, and someone
turns on the hot water in the kitchen, and you freeze your cookies until
they turn the watre off, right?

Same thing in a car. When you open the valve to allow hot water into the
heater core you're changing the dynamcis of the cooling system for a
minute or two.

Now, I have owned Toyotas, many models, for a long time. I also have a
Chrysler LHS and a Plymouth AWD Voyager. The Voyager has a heating
problem, and acts like you describe: when I step on the gas, the heat gets
better.

This is because engine RPMs are increasing and the water pump is
circulating the water better. You didn't mention which car; make or model
you're having this problem with. In my case, it is only the Voyager, and I
suspect a weak water pump. My Camry, the LHS, my Supra and my old ('85)
Celica don't exhibit this problem.

There are also a number of other factors which might come into play
here.  The most obvious is coolant level.  If the car is running low on
coolant, you'll get this kind of behavior.  You have to remember that
the heater core is basically another radiator, and that the cooling
system may not have enough coolant in the system to keep the heater core
"full" while going downhill, causing the reduced temperature coming
through the air vents.  When going uphill, the angle of the car probably
causes the heater core to fill up again and heat up, increasing the
heater temp again.  If coolant levels are fine, you may want to check
for blockages in the radiator passages, or perhaps check for air bubbles
in the cooling system.

But generally, I've never owned a car that under normal operation, the
engine temperature would vary SO much once the vehicle reached normal
operating temperature that it would noticeably affect how hot the heater
is.  Yes, there are small variations in engine temp based on outside are
temperature, how fast you're going and what accessories are running,
etc, but it's usually not enough of a change to make the heater air temp
noticeably cooler or warmer.

I wouldn't be so comfortable with a temp gauge that fluctuates TOO much,
expecially on newer cars.  A fuel injected engine works best within a
specific temperature range, and the idea of a cooling system isn't to
keep teh engine on ice, but to keep it not too hot, and not too cold.

Also, not all factory temp gauges are alike, nor are they the most
accurate. Certain vehicle models might have temperature gaguges that
report a wider range of temperatures, while others might just be
calibrated to be more concerned about whether the car is going to
overheat or not.

Well, yes: most major car manufacturers have preferred relationships
with suppliers that used to be a subsidiary of the automaker itself.
The "Big Three" as well as many foreign automakers chose long ago to
make their own gauge clusters and other sensors and components in-house,
and so separate divisions were made within those companies for that
purpose.  Ford eventually spun off their parts division (now known as
Visteon, currently in financial trouble), and GM did the same (Delphi,
now bankrupt but still manufacturing GM parts as well as XM and Sirius
satellite radios).  Chrysler's parts division (Mopar) is still a
DaimlerChrysler subsidiary. And each company has their own ideas and
philosophies on how such instruments should work.