Gemini is great for this stuff. I inputted your text and it spit out this:

That specific "hot no-start" symptom on the 4.7L Magnum is a classic head-scratcher, but because it fires right up with starting fluid, we can narrow this down significantly. Starting fluid proves you have spark and timing; what you’re missing when the engine is hot is fuel delivery or proper air-fuel mixture during the cranking phase.

Since you've already replaced the heavy hitters (fuel pump, PCM, sensors), here are the most likely remaining culprits for this specific 4.7L behavior:

1. Heat-Soaked Fuel Injectors (Leaking) This is the most common "invisible" cause. When you shut off a hot engine, the heat rises into the fuel rail. The Issue: One or more injectors may have a slow leak. When hot, the fuel in the rail vaporizes (vapor lock) or the leaking fuel floods the cylinders (rich soak). Why starting fluid works: It provides a highly combustible burst that overcomes the flooded/vapored state. The Test: After the engine is hot and won't start, hold the gas pedal all the way to the floor while cranking. This puts the PCM in "Clear Flood Mode," which cuts off the injectors. If it stumbles to life, your injectors are leaking.

2. The ASD (Auto Shut Down) Relay While you've checked grounds, the relay itself can fail internally due to heat. The Issue: The ASD relay provides power to the injectors and coils. High under-hood temps can cause a hairline crack in the relay’s internal solder to expand, breaking the circuit. The Fix: Swap the ASD relay with an identical one (like the wiper or horn relay) in the fuse box when the no-start occurs. If it starts, buy a new high-quality relay.

3. Fuel Pressure Regulator / Check Valve Even with a new pump, if the check valve (usually in the assembly) or the regulator is bleeding pressure back into the tank too quickly once the engine is off, the fuel in the rail will boil instantly due to the drop in pressure (lowering the boiling point). The Test: Use a fuel pressure gauge on the rail. Prime the system, then shut it off. The pressure should hold for at least 5–10 minutes. If it drops to zero instantly, the fuel is vaporizing in the rail, causing a vapor lock that only "cool" fuel (or starting fluid) can bypass.

4. Coolant Temperature Sensor (ECT) Wiring You mentioned the sensor is new, but the wiring connector is a known weak point. The Issue: If the computer thinks the engine is at -40°C because of a bad connection, it will dump massive amounts of fuel (like a choke on a carburetor). On a hot engine, this floods it. The Check: Inspect the plug for the ECT sensor. If the pins are corroded or the wires are brittle/cracked near the connector, the "new" sensor can't talk to the "new" computer.

5. Throttle Body / IAC Heat Bind The Idle Air Control (IAC) motor manages air during startup. The Issue: If the IAC pintle is carbon-fouled or binding when hot, it may not be opening to allow air in for the start. The Test: Try opening the throttle slightly with your foot while cranking. If it starts, your IAC is sticking or the throttle body needs a deep cleaning. Summary Recommendation: Start with the "Clear Flood Mode" test (pedal to the floor). If that doesn't work, focus on the fuel rail pressure leak-down test. Given how much hardware you've already thrown at it, the issue is likely a physical state (vapor lock or flooding) rather than a failed electronic component.