1996 Dodge Neon why is it getting hot?

Is your cooling fan working? The fan switch located on the motor near the thermostat could be a problem or the fan motor, or the relay, If the fan doesn't start, unplug it and run fused wires from the battery to the fan, it should run.
Neon 1. Turn ignition on. Using scan tool, actuate radiator fan relay. If fan motors do not operate, go to step 3) . If fan motors operate, condition required to set DTC does not exist. Check wire harnesses and connectors for broken, bent, pushed-out or corroded terminals. Repair as necessary and recheck system. If wire harnesses and connectors are okay, go to next step. 2. Continue using scan tool to activate motors. Wiggle harness and connectors between PCM harness connector and fan motor connector. If fan motor operation is not interrupted during wiggle check, inspect related harnesses. Check for chafed, pierced, or partially broken wires. If wires are okay, test is complete. If fan motor operation is interrupted, repair fault where wiggling caused interruption. 3. Continue using scan tool to activate fan motors. Using DVOM, backprobe fan relay connector terminal No. 2 (Dark Green wire). Fan relay is located on left front inner fender frame. If voltage does not cycle from zero to battery voltage, stop scan tool fan motor activation and go to next step. If voltage cycles from zero to battery voltage, check wire harness between fan relay and fan motors. If harness is okay, repair or replace fan motors. 4. Turn ignition off. Disconnect fan relay 4-pin connector. Turn ignition on. Check voltage at radiator fan relay connector terminal No. 4 (Gray wire). If voltage reading is 10 volts or greater, go to next step. If voltage reading is less than 10 volts, repair open in Gray wire or fuse No. 5 (30-amp). Recheck system. 5. Turn ignition off. Check resistance between fan relay connector terminal No. 1 (Black wire) and ground. If resistance is less than 5 ohms, go to next step. If resistance is 5 ohms or greater, repair open in Black wire. Recheck system. 6. Ensure ignition is off. Disconnect PCM 40-pin harness connector. Check resistance between PCM 40-pin harness connector terminal No. 18 (Light Green wire) and ground. See Fig. 8 . If resistance is 5 ohms or greater, go to next step. If resistance is less than 5 ohms, repair short to ground in Light Green wire. 7. Check resistance in Light Green wire between PCM 40-pin harness connector terminal No. 18 and fan relay 4-pin connector terminal No. 3. If resistance is less than 5 ohms, go to next step. If resistance is 5 ohms or greater, repair open in Light Green wire. 8. Connect fan relay 4-pin connector. Connect a jumper wire to PCM 40-pin harness connector terminal No. 18 (Light Green wire). Momentarily ground jumper wire. If fan motors operate, replace PCM and recheck system. If fan motors do not operate, replace fan relay and recheck system.

I hate to say this but Chrysler uses waterpumps with plastic impellers, you might want to look at that, rich running will not cause overheat Lean will. It could overheat the converter though. Try this to check for any more codes. Turn the key from off to on three times, on the fourth one leave it in the on position, the codes will display on the odometer, write em down and post em.
Or the check engine light will flash them.