I have changed the wires, plugs, cap and rotor, and points.

Runs really well when cold.

Only really happens when holding the car at around 2K RPM.

It accelerates well, and doesn't die on idle but acts like it wants too.

Fuel filter?

Didn't have your problem exactly, but chasing unsteadiness in performance as the car warmed up. When at full temperature the idle started to get dicey when turning on headlights.

Installed 123 distributor (with bluetooth for easy tuning) and all problems went away.

Worn throttle position sensor?

Clean and regrease advance plates in the distributor.
The “grease” is over 40 years old and makes the advance plate stick fully advanced when hot, which makes idle terrible.

Make sure that your valves are properly adjusted. I experienced similar behavior and found that the valves were too tight. Once it warmed up it created a negative gap so that the valves didn't close fully.

Nobody asks what kind of motor or carbs/FI?

It could be ignition related as Rich is suggesting, but it also sound like a fuel delivery / mixture problem to me. Worn TPS is also a possible bonus problem, assuming it still has the TPS.

Can you tell us more about your setup?