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Heater is an extra "radiator" so there could be a few things that can cause described symptom

If you let engine idle AFTER it is warmed up(heater off) does temp start to go up?
If so then could be failing fan clutch, but............temp would drop back down once you were moving, as radiator now has air flow again

It is possible that the bypass valve is blocked when closed, you can get a Coupler and two hose clamps to bypass the bypass, lol, and see if problem goes away.

And could be radiator is clogged up
After engine is fully warmed up and rad is hot, shut off engine and remove fan shroud, slide it back
Run your hand over the rad cooling fins and feel for cooler spots, those are blocked passages, you will feel the difference

Water pump on its last legs
If coolant is not changed regularly the water pump impeller blades get worn down, eaten away, but...............raising RPMs should cause better cooling if this were the case

 

 

You will never get the radiator fully cleaned out......... i have been there before not a ranger..........i pulled the radiator lay it down and poured half gall of castrol superclean into it use duct tape to seal the openings, leave cap on ... let it sit a few hours, sloshing it around every half hour, then shove a hose pipe into the cap end flush out......... it worked for me............. in the old days you could get it rodded out but they are plastic now, can not do that.... might need new rad if flush dont work

 

Some info on coolant
Until the early 1990's coolant was Silicate based, often "green" in color, although color is NOT universal, just a loose parameter some makers use, some do not
Silicates would start to break down after 2 years, so coolant needed to be changed every 2 years.

Then OAT(organic acid technology) coolant came along, this was usually Red/Pink, and lasted 5 years, often called "lifetime coolant", since car maker warranties for cooling system and engine was 5 years long, lol

Now we have HOAT(hybrid organic acid technology), still 5 year change interval and same "lifetime coolant".
HOAT uses silicates and OAT, so is a true Hybrid

Now the problem, you can NOT make your own Hybrid coolant, if Silicate based and OAT based are ever mixed in a cooling system you end up with a sludge.


1999 Ranger came with OAT(organic acid technology) based coolant, and some one probably added or changed it to Silicate(less expensive) coolant along the way so you end up with the sludge.
So now you pretty much have to use the more expensive HOAT coolant at least this first time after Flushing
HOAT won't sludge up if some Silicate or OAT remains in the block, it will in fact help bring it back into a fluid.
Then after 5 years you can change it to Silicate or OAT or stay with HOAT

I would just replace radiator, and also use an "Automatic" Radiator even if you have a manual trans, they are always Double core, some manuals had single core.

Simple test for clogged radiator is to drain it in the vehicle
Pull it out, then Flip it upside down
If ANY coolant/water comes out the rad cap or upper rad hose openings then it could ONLY have come from clogged tubes

Also best practice is to Reverse Heater core hoses at the firewall every few years, this Back Flushes the core when it is used, helps prevent clogged tubes
When a heater core tube gets clogged it reduces heat inside, of course, but.............it also means that tube no longer has anti-corrosion protection the circulating coolant provides, so it will corrode and then you get that smell and coolant leak inside the cab
So Reverse those hoses, try to keep those tubes open as long as possible

 

 

The other problem with the 3 litres is that the lower intake manifold at the back of the engine becomes blocked with rusty sludge.
If replacing the rad helps, but doesn't cure the problem, there is that to consider.

Go to the 17 minute mark and keep watching for a minute or two.

 

 

When you put the new rad in, don't fill it with ant-freeze mix, just use garden hose water for now, you're in South Carolina, so you don't have to worry about freezing.
Drive it for a few days or a week with just water.

Drain the water out buy pulling the bottom rad hose off, this makes a mess of course, but the idea is to clean the crud out of the block.
This sudden drain of coolant also helps to eliminate build up of rust sludge in the new rad, that has accumulated in the block and that has made its way to the rad.

Continue this procedure for as long as necessary until the water is clear, or reasonably clear.
This also helps with what I pointed out in the video.

One of the design flaws of the engine is that there are no drain taps to drain the block, the only way is to keep flushing things out.
If you ever replace the water pump, the holes to the block where the coolant is pumped into are exposed, if the front timing cover is removed.
Using a garden hose with the end cut off allows you to snake it in there and force the sludge out.
You can also make up a skinny end to a wet/dry shop vac and suck the sludgy water out.
With this method you can keep adding clean water and continue vacuuming until things are clean.

I've also used CLR (some use vinegar) to help break up the crap inside the engine and lower intake manifold.

 

 

 

Good work

Thanks for posting the update