Dear rlstites,
Good p.m. and may this find you well. The ECT - engine coolant temperature sensor - mounted in the head, below the intake manifold arms. towards the rear (driver's side, USA/Canada models) may have been damaged, when the car over-heated.
It may be sending the Engine Control Unit (ECU) a signal, that the coolant is "cold", after the coolant has warmed (or vice-versa). As a result of this erroneous signal, the fuel/air mix is too rich (which might account for the smell of gas) or lean (too little fuel). Typically, though, this signal will be consistent.
Another possibility, which should be checked first: a Dirty Idle Air Control Valve (on bracket below/beside the intake manifold, driver's side of the engine bay). See the FAQs, under FEATURES, above, for instructions on cleaning it.
Because changing the ECT is time-consuming, start with cleaning the IACV. Then, check the RPM sensor. If it is the original (it likely will have a yellow painted marking around the harness circumference, at some point; later units have a white band), it should be replaced. The insulation becomes brittle, allowing moisture to get in, which causes shorts. When the signal is lost, the fuel pump shuts down. That, plainly, could cause the engine to run "rough".
Hope this helps. Post back, with your findings.
Yours faithfully,
spook
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