Car over heats when going up long hills

the pressure sensor is the barometric sensor ( baro)
it reads the atmospheric pressure and reports to the ECM to adjust the air fuel mixture according to the atmospheric pressure
as in going up a hill or mountain or when the air is very hot and the air is thin

If it has high mileage on it probably is the catalytic converter is stopped up. A dead give away is losing power going up hills and not shifting like it used to. A easy test is to put your hand over the exhaust pipe wear a glove as it may be hot. Then have a friend give it gas if it is stopped up you will be able to hold the exhaust from coming out. That is just a simple test but more then likely it is stopped up . You can get a after market cat for about half the price of a new one . Good luck.

Check for codes

Most likely half the ignition coils have failed

The Egr Valve could be gone as well

Have to change spark plugs every 3 years
Clean MAF Sensor once a year

Can't just drive it until you have a problem

Needs to be in the shop a couple times a year,
just like you go to a doctor

First question is what constitutes "overheating".
Since the car has been parked for years, the thermostat could be sticking closed.
The cooling system could have air pockets and need to be bled.
The water pump may be corroded inside and not pumping enough volume.
If the gauge goes above half way, the fans should start up. But half way should be more or less normal, not hot yet.
I would look at flow problems first, beginning with removing the thermostat and driving it without one for a few days. Also check and see if there is a process to bleed the cooling system of air.

you mention big hills, and other wise no problem, you may be taxing the transmission , have a trans cooler installed, it may cure all your problems, and good for the trans, heat is the trans biggest killer

Plugged fuel filter? Going up hill will demand more fuel so maybe the filter is restricting high flow.

Change your gearbox oil, and clean out the oil strainer.
Should help.

( On some models, you have to remove the gearbox oil pan to clean the strainer )

Try changing fuel filter. There could be one large one next to tank or inside frame rail.

It sounds normal, but perhaps the radiator is a little small. Make sure the core is clean by blowing it out with compressed air (from the engine side) to clear out bugs and other debris. Make sure the overflow/reserve tank is at the proper level. Check the coolant level in the radiator when engine cold--it should be right at the top of the filler. These are all preventive, not a cure for anything.

Its overheating when you go up long hills because the engine is not getting adaquete air in the system. The radiator is angled to get optimal air a certain way. It may overheat but you shouldn't start seeing smoke.