1959 Ford Fairlane 500 Getting Hot Quickly?

I own a 1959 Ford Fairlane (AKA, Galaxie), I recently had the carburetor rebuilt and the generator exchanged for an alternator, I also got an oil change done to it.

It drives like a charm, and takes normal gas, the only thing I've noticed is that the heat gauge will raise to about 3/4ths hot and sometimes a little over that and I'm concerned that it's borderline over heating. I never drive long enough to find it out the hard way, I only take it into town and back for chores and what not.

Is there a way to solve this, or is that the normal temperature for the model year?

Thanks!

PS: The Radiator and the Coolant haven't been done since the previous owner, I'm suspicious one or the other might be the cause, I just need a second opinion.

It does not get hot in the mornings, and I live in Texas and right now it's the dead of summer. It only gets hot in the middle of the day (usually around 80 - 100 degrees out). It does not make any loud noises except for when it's over 3/4ths hot, but even still it does not do anything super loud, as I said it drives like a charm!

First thing to check is the thermostat. They come In several temperature ranges, and all of them loose accuracy with age.

The second thing to check is the radiator. It can become partially clogged with rust over time. The rust is from the inside of the engine and carried to the radiator by the water / coolant mixture and deposited in the radiator core.

It is not unusual for a temp gage to reach 3/4 of the range. Often they will go a little higher, then the thermostat opens and the temperature gage drops back down. The total time for an engine to get "warmed up" is often in excess of fifteen minutes.
If you do not know the age of the coolant I would suggest an engine flush and replacing the coolant with newer replacements. Also do the thermostat while you are at it. Newer fluids for the cooling system lubricate the pump better and prolong its life. They have the additional benefit of better rust protection for the coolant passages.
Make sure the radiator fins are not clogged with dead bugs or other junk too.

The gauge on the dash may not accurately show the coolant temperature
The coolant may just be low. (do not check it when it is hot)
The Thermostat may be sticking
The coolant may be the original from 1959

Throw away your thermostat

The easiest way to check this is with a digital/laser thermometer available from your local auto parts supply (they are quite inexpensive now and readily available), or, have someone who has one check it for you. As the engine warms, keep checking engine temperature near the thermostat housing (where the upper radiator hose attaches to the engine). Depending on the temperature rating of the thermostat (+5 degrees F) you will know if the thermostat is defective. If the thermostat is opening at it's normal temperature rating (or close to it) check the temperature of the radiator. I believe your vehicle will have a vertical flow radiator (the main coolant channels running from top to bottom). Check the temperature difference of the radiator from top to bottom - a difference of 10-15 degrees F is normal. Should you see a difference of say 25 degrees or more, the radiator is partially blocked and the coolant is not flowing through it properly for efficient cooling. Don't forget to let the engine run long enough for the thermostat to open a couple times and allow the cooling system to do its job, as efficiently as it can.

You need a way to accurately check the temperature.

Your car should probably have a 180° F thermostat and should probably run around 190°.

If you are driving with the temperature gauge at 3/4 scale and you turn on your heater, to maximum hot and high blower speed, does the gauge drop at all?

Does your engine have a thermostatically controlled radiator fan (a "clutch" fan)?

Does your radiator fan have a full shroud around it?

It's possible that your thermostat is faulty. They don't last forever. A thermostat operates in a strange way. Read about it.

It's possible that your radiator has internal flow problems or has internal thermal insulation (dirt) on the tubes.

It's possible that the radiator fins on the outside of the radiator are rotten from age and are not conducting heat away from the tubes efficiently.